{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've been trying to use the analytical (Buckley-Leverett) solution of the two-phase flow in porous media to fit the Corey-type relative permeability model to the experimental oil recovery data. In this post, I'm going to compare the numerical solution of the same model with the analytical results. You can find the codes that I have written in [this github repository](https://github.com/simulkade/peteng). Here, I only call the codes and compare the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the input parameters and the functions\n",
    "using Roots, PyPlot, Dierckx, JFVM\n",
    "import JSON, JLD\n",
    "include(\"rel_perms.jl\")\n",
    "include(\"forced_imbibition_corey.jl\")\n",
    "include(\"frac_flow_funcs.jl\")\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input parameters are stored in the `input_params_BL.jld` file, that can be loaded by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14-element Array{Symbol,1}:\n",
       " :L_core  \n",
       " :kro0    \n",
       " :krw0    \n",
       " :mu_oil  \n",
       " :mu_water\n",
       " :no      \n",
       " :nw      \n",
       " :perm_ave\n",
       " :poros   \n",
       " :pv_inj  \n",
       " :sor     \n",
       " :swc     \n",
       " :swi     \n",
       " :u_inj   "
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JLD.@load \"input_params_BL.jld\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the functions for the analytical and numerical solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "# call the functions\n",
    "# numerical solution (finite volume)\n",
    "(t_num, R_num, sw_prf)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj, Nx=50)\n",
    "\n",
    "# Analytical solution (BL)\n",
    "(xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "  muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "  k=perm_ave, swc=swc, sor=sor, kro0=kro0, no=no, \n",
    "  krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj)\n",
    "IJulia.clear_output() # only to clear the output from the previous function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can plot the results and compare the solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qfSeCCoaaO5hgrmO8Yz3djKPerx20k1jmHs1y92j22F0aPD/V2IiIgo6IBCyQVRvwdElda25hgmMdY81NtDdKvF87bbfhQ/dw3nWPYa19ZYNWblRjIyLVKeiIyEUF2vpdpSMnGO/YwHhzHSPNrUQb51d5jtntyHEPZoWVyb+sgbiICnheWq0RkbpQ0BGRGgW6agM2vY1DTDDXMcGxngxzt99X91gprLAyWeHOZIN9BVaAKzdtI01uGdBZqzUiEhAFHREBArvtu4qJRaaxk/GO9Yw319HDLPL7+karNyvcmXxkDal3+7eKh0WkIRR0RFqxQM62qRKDizHmV0ww13GDYyOXGae9X3PZEay2+rPCyuRj92CK6RDQfNq3iWTayO5q+RaRoFHQEWmFAt2WuoxT3ODYyARzPaPNr2hjnA9EJ+1YPrGuZoXbU29T11u/46Id3JnZTTU2ItKoFHREWrj6FhP3MAoYX9kCnml87XflwgGro6fexsrkS+tKKgL4nxJtRYlIU1LQEWmhAl21MbDIMHYz3rGeCeY6epuH/b7+lZXGCvcQVliZ5NmXU9d6G7V8i0goNYugs2jRIubPn09hYSGDBg3ipZdeYtiwYTWOfeONN5g+fbrfs+joaEpLS5tiqiLNXlXAeeVfuy+5ahNNGSPNrYw31zHOsZFOxknv18ptB59b/SrrbTI5TFKd55AYG8nkjK6MS09RsBGRkAp50Fm6dClZWVksXryY4cOHs2DBAm666SZ27NhBp06danwnPj6eHTt2eD83DP2PqEhdA04CZ7jB3MgExzquNbcQa7i8Xzttt2GlNYgV7iGstAbhJLZOP1ut3yLSXIU86Lzwwgvcf//93lWaxYsX8+GHH7JkyRIee+yxGt8xDIOUlJSmnKZIsxLo1QvdjCNMMNcz3lzPUHO734WZBXYiH7sH8w9rCJ9b6ZSr3kZEWpCQBp2ysjLWr1/PnDlzvM9M02TcuHGsWbOm1vfOnDlD9+7dsSyLwYMH8/TTT3PVVVfVONblcuFynf8vVqfTGbxfQKSJ1b3uxqa/ke+tt+lnHvD7ap6VWnl43xC+sntQl3ob3fYtIuEopEHn6NGjuN1ukpOT/Z4nJyezffv2Gt+58sorWbJkCQMHDuTUqVM899xzjBw5kq1bt9KtW7cLxs+bN48nn3yyUeYv0lTqsi0VRTnDzTzGm+sZ51hPF+P4+fdtgy/tvqxwZ/IPK5MDdnKN36MmWrURkXAW8q2rQI0YMYIRI0Z4Px85ciT9+vXjlVde4amnnrpg/Jw5c8jKyvJ+7nQ6SU1NbZK5ijSE72F+f6xlW8rAYoK5jkmO1YwxvyLOOF+Uf9aO5lNrICvcmXxiXc1J2l3yZ+psGxFpaUIadJKSknA4HBQV+R8bX1RUVOcanMjISK6++mp27dpV49ejo6OJjo5u8FxFmkrdtqdsJpjrmB3xF/qZ+71Pj9jtyXFfzQork9VW/zpflhkb5eAH1/bUqo2ItDghDTpRUVFkZmaSk5PDpEmTALAsi5ycHGbOnFmn7+F2u/nqq6+45ZZbGnOqIo3uUttTkVQwzMzjRnMjN5ob6G4eAcBpt+Et93j+7h5Grp2GHcBlmdqWEpGWLuRbV1lZWUybNo0hQ4YwbNgwFixYQElJibcLa+rUqXTt2pV58+YB8Itf/IJrrrmG3r17c/LkSebPn8++ffv4/ve/H8pfQyQggZxWfJWxlx9EfMAN5kbaGee8z0vsaF5338yrFbdyirhL/kwVE4tIaxTyoDNlyhSKi4t5/PHHKSwsJCMjg+zsbG+B8v79+zHN8/+FeuLECe6//34KCwvp0KEDmZmZfPbZZ6Snp4fqVxCps0BOK+5v7GFWxLuMd6z3Piu2E/jEfTU51tX82xrAWWIu+TO1LSUirZlh27Z96WEth9PpJCEhgVOnThEfHx/q6UgrEchpxQOMPcyK+AvjHBs979oG71sjeKPiZjbbPeu8NaVtKRFpSer753fIV3REWrJAAs4gYxezIpZxg2OT513b4D1rFAsrJrHH7lKnn6erF0RE/CnoiARZXdrCfQ02djIrYhnXObYAUGGb3oCTb3e+6Lu6ekFE5OIUdESCJNDbwjONHcyKWMa1jq8AT8B51z2ahe5J7LMvfryCtqVEROpGQUekgQLZngIYamxnVsRfGO3YCnhuCV/mHsMi9+3sv8iJxXHRDqYMSdW2lIhIABR0ROoh0O0pgOFGHrMi/sJIxzbAE3D+5L6W/3XfzkG7U63vqWtKRKT+FHREAhDo9hTYjDC3MStiGdeYeQCU2Q7+5L6e/624jUN0rPVNBRwRkYZT0BGpg0C3p8BmpLmVWRHLGG56Lqh12RH80X09L1fcxmGSan1T9TciIsGjoCNyCdm5BTy27CtOnq3bCs5oM5dZEX9hqLkT8AScd9xjWVxxGwVc5jdapxWLiDQuBR2Ri/jblgIeeHtDHUbaXGtuYVbEMjLNrwFw2ZG87b6BxRUTKSLRb7S2pUREmoaCjkg1VYXGH20t4Ldr9l1itM315mZmRSzjanMXAKV2JG+7b2RxxUSO0MFvtLalRESaloKOSKXACo1txpqbmBXxFzLMPQCcs6P4vftGXqn4JsU+AUdt4SIioaOgI61eYIXGNjeaG3g44l0G+QSc37nH85uKb3KUBO9IbU+JiISego60WoEGnPHmeh6OWMYAcy8AZ+1o3nSP59WKWznmE3C0PSUi0nwo6EirEuhBfwYWEyoDzlWmp16nxI7mTfcEXq24leN4btDV9pSISPOkoCOtRnZuAU++v42CU6WXHGtgcbP5JQ9HvEs/cz8AZ+wY3nDfxGsV3+BEZcDR9pSISPOmoCOtQt3bxGGMuYWfRvyevuYBAE7bbXjdfROvVdzCKeIAMIBZN/bhoRsVcEREmjMFHWnR3JbNizlf82LO15cc2wEnP498izsc/wbAabfhdfc3eK3iZpyVAafKoruv5paBXRplziIiEjwKOtIiBVpoPMlczeORb5JonMGyDX7rnsD/VHzrgoDTOSGGuRPTubl/58abvIiIBI2CjrQ4gVzZ0M04wi8jlnCdYwsAeVYqc8rvZ5Pd2ztGhcYiIuFLQUdajKpVnP/5eOclxzpwM92RTVbEn2lruHDZkfy6YjK/cX+Tisr/t1ChsYhI+FPQkbBXFXCW/HsPp0ov3i4OcJWxl3mRrzLQzAdgjTudn1TcR77t2Y5SwBERaTkUdCRsBVaHAzG4eCRiGd93fEiEYXHKbssvK+7hj+7rAUMH/YmItEAKOhKWAqnDARhp5jIv4v/obh4B4AP3NTxZPpWjtGf6yDQmXKX6GxGRlkhBR8JKIHU4AO05zc8if8+3Hf8C4LCdyM/Lp5NjZQLwv2oTFxFp0RR0JGxk5xbwxF+3Uuh01WG0zW3mZzwe+TuSDCeWbfCmezzPVXyHM7SlQ9tI5t0xQG3iIiItnIKOhIVATjbuSjH/L3IJYx2bAdhhdWNO+ffZYF9BbJSD2So0FhFpNRR0pNn725bDzPzDxkuOM7GY5viI/4r4I7GGC5cdwUsVk3nFPZHYNm2YrUJjEZFWR0FHmrXs3AIeePvSIecyTvHryIWMdmwF4AurLz8pv4/ddldmj+ujgCMi0kop6Eiz5bZsnnx/2yXHZRo7WBT1IinGCc7a0fy/inv5g3ss7dtGs1h1OCIirZqCjjRba/OPU3Cq9CIjbL7v+BuPRfyBCMNil9WFH5Y/QkFkdx4ZqzocERFR0JFm7Mjp2kNOO84yP/IVbnZ8CcB77pE84/ghd93YTwFHRES8FHSk2erULqbG5/2MfbwcuYA0swiXHcFTFf9Bx+tn8O8br1DAERERPwo60mydKHFhGmDZ55+NNr/ilcgXiDVcHLSTmFk+ix/cdSe3DFQdjoiIXMgM9QREapKdW8CDb2/0CznfML9gSeSviDVc/Nt9Fbe6nuYHd31bIUdERGqlFR1pdqq6rXwyDt801/DryIU4DJsP3MP5r4oHeOHu4Qo5IiJyUQo60uxU77bKNHbwfOTLOAybP1SM5acV92Fh0iE2KoSzFBGRcKCgI82Ob7dVO87yUtRLRBsVZLuH8pOK+7Ard1wv1pUlIiICqtGRZsi322pWxF/oYhwn30pmdvkMb8ipPk5ERKQmWtGRZqeq2yrOPsN/OD4GYG7Ff3IOT7AxgJSEGIb1SAzhLEVEJBwo6EizUtVtZQPfdHxBtFFOnnU5/7IG+o2bOzFdZ+aIiMglaetKmo3q3VaTHasAWOYejWcdB0wDFt09WPdXiYhInSjoSLPh222VahQx1NyJZRu85x7lHWPZqNtKRETqTEFHmg3fLqpJ5moAVltXcYQOtY4TERG5mDrV6Lz44osBf+Pp06fTrl27gN+T1ispLrry72wmO/4NwLvu0ReMU7eViIjUVZ2CziOPPEK3bt1wOBx1+qYHDhzgm9/8poKO1Fl2bgFP/HUrABnGbnqahZy1o8m2hnnHqNtKREQCVeetq3Xr1pGfn1+njzZt2gQ0iUWLFpGWlkZMTAzDhw9n7dq1dXrvnXfewTAMJk2aFNDPk+YlO7eAGW9toNDpAmBS5WrOP6xMzvq0lIO6rUREJDB1Cjpz584lLi6uzt/0Jz/5CYmJdfuv7qVLl5KVlcXcuXPZsGEDgwYN4qabbuLIkSMXfW/v3r3813/9F2PGjKnzvKT5qd5pFUEFEx1rAHjXff6fbUpCDC/fq24rEREJjGHbtn3pYY1n+PDhDB06lIULFwJgWRapqak89NBDPPbYYzW+43a7ufbaa/ne977HqlWrOHnyJMuXL6/Tz3M6nSQkJHDq1Cni4+OD9ntI/azZfYzvvvq59/MbzfW8FvU8xXYC17gW4sazXfr7+4Yzqk9SqKYpIiIhVt8/vxvUdfXMM89w8uTJer9fVlbG+vXrGTdu3PkJmSbjxo1jzZo1tb73i1/8gk6dOnHfffdd8me4XC6cTqffhzQf1TuoJjs83VbvuUd6Qw7A0RJXk85LRERahgYFnaeffprjx4/X+/2jR4/idrtJTk72e56cnExhYWGN7/z73//mtdde49VXX63Tz5g3bx4JCQnej9TU1HrPV4LPt4OqHWcZb64HLuy2UqeViIjUR4OCTlPvep0+fZr/+I//4NVXXyUpqW7bGHPmzOHUqVPejwMHDjTyLCUQw3okkhLvCTHfqLzyYafVla12GuApQu6sTisREamnkN51lZSUhMPhoKioyO95UVERKSkpF4zfvXs3e/fuZeLEid5nlmUBEBERwY4dO+jVq5ffO9HR0URHRyPN04pthZRWuAGYXHlIoKcI2VCnlYiINFiDVnS2bdtG9+7d6/1+VFQUmZmZ5OTkeJ9ZlkVOTg4jRoy4YHzfvn356quv2LRpk/fjtttuY+zYsWzatEnbUmGmqq385NlyunCUEY5tgKc+B6B920h1WomISIM0aEUnGMEiKyuLadOmMWTIEIYNG8aCBQsoKSlh+vTpAEydOpWuXbsyb948YmJi6N+/v9/77du3B7jguTRv1dvKJ1UWIa9xp3MYz7ZkdITJ+PQLV/ZERETqqk5BJzExkZ07d9a5Lubyyy9n1apVdVrtmTJlCsXFxTz++OMUFhaSkZFBdna2t0B5//79mKau5GppfC/w9L3yYZl1vgi50Olibf5xRvS6LAQzFBGRlqBOQefkyZP8/e9/JyEhoU7f9NixY7jd7jpPYubMmcycObPGr61cufKi777xxht1/jnSfPi2lV9l7KWPeYhSO5Js97Bax4mIiASqzltX06ZNa8x5SCvj2y5+R+VqzsdWJqdpW+s4ERGRQNUp6FR1NokEy4kSF6YBhu3mNsdnACzzOTtHF3iKiEgwqPhFmlx2bgEPvr0Ry4bRZi4djVMcs9vxL2ug3zi1lYuISEMp6EiTqt5tNdmxCoD33SOoqFxgNA1YdLfaykVEpOEUdKRJ+XZbxXKOm8x1gP+VD5YNHWKjQjI/ERFpWRR0pEn5dlHdZH5JG6OM3VZnNtu9ah0nIiJSXwEFnYqKCt4QIwj6AAAgAElEQVR8880LrmwQqSvfLqqqs3OWu0cBRq3jRERE6iugoBMREcEPf/hDSkv1X9tSP1XdVskcZ5S5FYB3Lf9uK13iKSIiwRLw1tWwYcPYtGlTY8xFWjjfbqvbHasxDZu11pUctDv5jVO3lYiIBEvAd1098MADZGVlceDAATIzM4mNjfX7+sCBA2t5U1qzC7utPHdbLfcpQjYNWPhddVuJiEjwBBx07rrrLgAefvhh7zPDMLBtG8MwArr6QVoP326rvsZ++pn7cdkRfOAe7h2jbisREQm2gINOfn5+Y8xDWjjfLqqqs3M+sa7GSVyt40RERBoq4KBTlxvJRapLiosGwMTi9sorH3y3raqo20pERIIp4KADsHv3bhYsWEBeXh4A6enpzJo1i169el3iTWmNsnMLeOKvng6rEeZWUowTnLRj+aeV4R2ju61ERKQxBNx19dFHH5Gens7atWsZOHAgAwcO5IsvvuCqq65ixYoVjTFHCWPZuQXMeGsDhU4XcP6m8g/c11BGJHD+BB11W4mISLAFvKLz2GOPMXv2bJ555pkLnj/66KOMHz8+aJOT8Fa906oNpdxkfgnAMvcY77iUhBjmTkxXt5WIiARdwCs6eXl53HfffRc8/973vse2bduCMilpGXw7rQDGm+uJM0rZZ3Vig93H+/y5bw9SyBERkUYRcNDp2LFjjQcGbtq0iU6dOtXwhrRW1Tuoqratlluj8b3y4WiJqymnJSIirUjAW1f3338/P/jBD9izZw8jR44EYPXq1Tz77LNkZWUFfYISvnw7qDpykjHmFgDedY+qdZyIiEgwBRx0fv7zn9OuXTuef/555syZA0CXLl144okn/A4RFBnWI5GU+BgKnaVMdKzBYdhstHqz1/ZsU6nTSkREGlvAQccwDGbPns3s2bM5ffo0AO3atQv6xCT8rdhWSGmF56TsqkMCl1WenaNOKxERaQoB1+jccMMNnDx5EvAEnKqQ43Q6ueGGG4I7OwlbVW3lJ8+W09s4yABzL+W2gw/c1wDQvm0kL9+re61ERKRxBRx0Vq5cSVlZ2QXPS0tLWbVqVVAmJeHtwgs8PUXIK61BnCAegOgIk/HpKSGaoYiItBZ13rrasmWL9++3bdtGYWGh93O32012djZdu3YN7uwkLPm2lRs+Vz6863PlQ6HTxdr844zodVlI5igiIq1DnYNORkYGhmFgGEaNW1Rt2rThpZdeCurkJDz5tpUPN7fTzTiK025LjjW41nEiIiKNoc5BJz8/H9u26dmzJ2vXrqVjx47er0VFRdGpUyccDkejTFLCi2+7+CTTs231oXs4LqJqHSciItIY6hx0qm4ttyyr0SYjLcOJEhemAZF2Gbc4vgD8bypXW7mIiDSVgIuR582bx5IlSy54vmTJEp599tmgTErCV3ZuAQ++vRHLhnHmBuKNcxy0k1hrX+k3Tm3lIiLSFAIOOq+88gp9+/a94PlVV13F4sWLgzIpCU8Xdlt5uvCWu0dhV/6rZhqw6G61lYuISNMIOOgUFhbSufOFf0h17NiRgoKCoExKwpNvt1UiTq7zXvlwftvKsqFDbFSN74uIiARbwEEnNTWV1atXX/B89erVdOnSJSiTkvDk20X1TccaIg03W6we7La71jpORESkMdXrUs9HHnmE8vJyb5t5Tk4OP/7xj/nRj34U9AlK+PDtoqq6qdx3NaemcSIiIo0p4KDz3//93xw7dowHHnjAe0JyTEwMjz76qPeST2mdqrqtulNAhrmbCtvkffdI79fVbSUiIk2tXpd6Pvvss/z85z8nLy+PNm3a0KdPH6KjoxtjfhImqrqtbGBShGc1Z5U1gKMk+I1Tt5WIiDSlgINOlbi4OIYOHRrMuUiY8u+2splsVm1bjfGOMQ1Y+F11W4mISNOqV9BZt24df/zjH9m/f/8FF3wuW7YsKBOT8OHbbZVp7ORys5gzdgz/sDK9Y9RtJSIioRBw19U777zDyJEjycvL491336W8vJytW7fyySefkJCQcOlvIC2ObxdVVRFytjWMUqJrHSciItIUAg46Tz/9NP/zP//D+++/T1RUFL/+9a/Zvn073/nOd7j88ssbY47SzFV1UUVRzq2OzwFYpm4rERFpBgIOOrt37+bWW28FPJd5lpSUYBgGs2fP5je/+U3QJyjNX2b3DiTGRjHW3Eh7o4QCO5HPrXTv1w2gs7qtREQkBAIOOh06dOD06dMAdO3aldzcXABOnjzJ2bNngzs7afaycwu4bv4/OV5SxmSH5yDJ99wjsSr/1arqr1K3lYiIhELAxcjXXnstK1asYMCAAdx5553MmjWLTz75hBUrVnDjjTc2xhylmcrOLWDGWxuwgQTOcIO5AfA/JDAlIYa5E9PVbSUiIiERcNBZuHAhpaWeotKf/vSnREZG8tlnn/Gtb32Ln/3sZ0GfoDRP1S/w/Kbjc6IMN9us7uywPbVaibGRfPrfY4mKCHjhUEREJCjqFHSysrJ46qmniI2NJTc3l5EjPafdmqbJY4891qgTlObJt6UcYJL3yodR3mfHS8pZv+8EI3pd1uTzExERgTrW6Lz00kucOXMGgLFjx3L8+PFGnZQ0f76t4qlGEUPNnbhtg/d8gk71cSIiIk2tTis6aWlpvPjii0yYMAHbtlmzZg0dOnSocey1114b1AlK8+TbKj7Z9BQhr7b6c4QOtY4TERFpanVa0Zk/fz6vvfYaY8eOxTAMJk+ezPXXX3/Bx9ixY+s1iUWLFpGWlkZMTAzDhw9n7dq1tY5dtmwZQ4YMoX379sTGxpKRkcHvfve7ev1cqb+qCzzB9m5bLfdZzVFLuYiINAd1CjqTJk2isLAQp9OJbdvs2LGDEydOXPBRny2tpUuXkpWVxdy5c9mwYQODBg3ipptu4siRIzWOT0xM5Kc//Slr1qxhy5YtTJ8+nenTp/PRRx8F/LOlfqou8LRsyDB209Ms5KwdTbY1zG+cWspFRCTUDNu27UsPO+/TTz9l1KhRRETU+z5QP8OHD2fo0KEsXLgQAMuySE1N5aGHHqpzofPgwYO59dZbeeqppy451ul0kpCQwKlTp4iPj2/Q3Fsjt2Uz+tlPvIXIT0a8zrSIFbzrHsXs8geB8xd43jJQLeUiIhIc9f3zO+C+3+uuuy5oIaesrIz169czbty48xMyTcaNG8eaNWsu+b5t2+Tk5LBjx45aa4NcLhdOp9PvQ+rPt9sqkgomOjz/nHzPztEFniIi0lyE9ICTo0eP4na7SU5O9nuenJxMYWFhre+dOnWKuLg4oqKiuPXWW3nppZcYP358jWPnzZtHQkKC9yM1NTWov0Nr49tFda25mUTjDMV2Aqut/rWOExERCZWwPMmtXbt2bNq0iS+//JJf/vKXZGVlsXLlyhrHzpkzh1OnTnk/Dhw40LSTbWH8uq0qi5Dfc4/EjaPWcSIiIqESnD2oekpKSsLhcFBUVOT3vKioiJSUlFrfM02T3r17A5CRkUFeXh7z5s3j+uuvv2BsdHQ00dHRQZ13a1bVbRVnlzDee+XDGO/XDTzXPqjbSkREmoOAV3Ref/31oF3eGRUVRWZmJjk5Od5nlmWRk5PDiBEj6vx9LMvC5XIFZU5SO99uq5sda4k2ytlpdWWr3d1vnLqtRESkuQg46Dz22GOkpKRw33338dlnnzV4AllZWbz66qv89re/JS8vjxkzZlBSUsL06dMBmDp1KnPmzPGOnzdvHitWrGDPnj3k5eXx/PPP87vf/Y577723wXOR2lW/2+oO75UPY6i6o9w0YNHdg3WBp4iINBsBb10dOnSI999/nzfeeIPrr7+enj17Mn36dKZNm3bR7abaTJkyheLiYh5//HEKCwvJyMggOzvbW6C8f/9+TPN8HispKeGBBx7g4MGDtGnThr59+/LWW28xZcqUgH+21J1vt1VXirnGzAP8DwlUt5WIiDQ3AZ+j46uoqIi33nqL3/72t2zfvp2bb76Z++67j4kTJ/qFk+ZE5+jUz3ubDjHrnU0APOB4jx9HLmWNO53vlvvfWP/ruzK4PaNrKKYoIiItWJOdo+MrOTmZ0aNHM2LECEzT5KuvvmLatGn06tWr1i4oCU9JcVUF3ba322qZNfqCceq2EhGR5qReQaeoqIjnnnuOq666iuuvvx6n08kHH3xAfn4+hw4d4jvf+Q7Tpk0L9lwlRLJzC/jRHz2rOf2NfPqYhyi1I8l2n7/yQXdbiYhIcxRwjc7EiRP56KOPuOKKK7j//vuZOnUqiYnn/3CLjY3lRz/6EfPnzw/qRCU0snMLmPHWhguKkD+2MjlNW6CqFFndViIi0vwEHHQ6derEp59+etH2744dO5Kfn9+giUnoVe+0cuBmosPTabfM58qHlIQY5k5MV7eViIg0OwEFnfLycvbu3UtSUtJFxxmGQffu3S86Rpo/304rgDHmV3Q0nBy14/mXNdD7/LlvD2JUn4v/OyEiIhIKAdXoREZGsmXLlsaaizQz1e+rqipCft89ggqfjHy0RIc1iohI8xRwMfK9997La6+91hhzkWbGt4MqlnNMMNcB/mfnVB8nIiLSnARco1NRUcGSJUv4+OOPyczMJDY21u/rL7zwQtAmJ6E1rEciKfExFDpLudn8kjZGGbutzmy2ewG610pERJq/gINObm4ugwcPBmDnzp1+XzMMddy0JCu2FVJa4QZgsmMVAO+6RwOGOq1ERCQsBBx0/vnPfzbGPKSZ8W0rT+Y4I81tACy3PNtW7dtGMu+OAeq0EhGRZq3eJyPv2rWLjz76iHPnzgHQgJskpJmp3lZ+u2M1pmGz1rqSg3YnAKIjTManB363mYiISFMKOOgcO3aMG2+8kSuuuIJbbrmFgoICAO677z5+9KMfBX2C0vSqt5VP9t5Ufv7snEKni7X5x5t8biIiIoEIOOjMnj2byMhI9u/fT9u2bb3Pp0yZQnZ2dlAnJ6Hh21bez9hHP/MALjuCD93Dax0nIiLSHAVco/OPf/yDjz76iG7duvk979OnD/v27QvaxCR0fNvFJ1Wu5nxiXY2TuFrHiYiINEcBB52SkhK/lZwqx48fJzo6uoY3JNycKHFhGoBtcXvllQ++21ZqKxcRkXAR8NbVmDFjePPNN72fG4aBZVn86le/YuzYsUGdnDS97NwCHnx7I5YNI82tpBgnOGHH8U/rar9xaisXEZFwEPCKzq9+9StuvPFG1q1bR1lZGT/+8Y/ZunUrx48fZ/Xq1Y0xR2ki1butqoqQP3QPp7zyXxXTgIXfHay2chERCQsBr+j079+fnTt3Mnr0aG6//XZKSkq444472LhxI7169WqMOUoT8e22akMpN5trAVjmHuMdY9nQITYqJPMTEREJVMArOgAJCQn89Kc/DfZcJMR8u6gmmOuINVzsszqxwe5T6zgREZHmLOAVnd69e/PEE0/w9ddfN8Z8JIR8u6gmOzzbkMstz5UPtY0TERFpzgIOOg8++CAffvghV155JUOHDuXXv/41hYWFjTE3aWJV3VYdOckYcwsA7/rcVG4AndVtJSIiYaReBwZ++eWXbN++nVtuuYVFixaRmprKhAkT/LqxJLz4dlvd5vgMh2GzwerNXtu/6FjdViIiEk7qfdfVFVdcwZNPPsnOnTtZtWoVxcXFTJ8+PZhzkyZSW7eV79k5pgGL7la3lYiIhJd6FSNXWbt2LW+//TZLly7F6XRy5513Bmte0oR8u636GAfpb+6l3Hbwgfsa7xh1W4mISDgKOOjs3LmT3//+9/zhD38gPz+fG264gWeffZY77riDuLi4S38DaXZ8u6iqVnNWWhmcIL7WcSIiIuEg4KDTt29fhg4dyoMPPshdd91FcnJyY8xLmlBSnOfqDgOL2yu7rZb5bFtVUbeViIiEm4CDzo4dO+jTp8+lB0pYyM4t4Im/bgVguLmdrsYxnHZbPvG58kF3W4mISLgKOOhUhZz169eTl5cHQHp6OoMHDw7uzKTRZecWMOOtDeeLkM3zVz648NTjVPVXqdtKRETCUcBB58iRI0yZMoVPP/2U9u3bA3Dy5EnGjh3LO++8Q8eOHYM+SQm+6p1W0ZTxDccXgH+3VUpCDHMnpqvbSkREwlLA7eUPPfQQZ86c8V7kefz4cXJzc3E6nTz88MONMUdpBL6dVgDjzA3EG+c4aCfxpX2l9/lz3x6kkCMiImEr4BWd7OxsPv74Y/r16+d9lp6ezqJFi5gwYUJQJyeNp3oH1WTHKgCWu0dh++TfoyWuJp2XiIhIMAW8omNZFpGRkRc8j4yMxLKsoExKGp9vB1UiTq7zXvkwutZxIiIi4SbgoHPDDTcwa9YsDh8+7H126NAhZs+ezY033hjUyUnjGdYjkZR4T4iZ6FhDpOFmi9WD3XZXQPdaiYhIyxBw0Fm4cCFOp5O0tDR69epFr1696NGjB06nk5deeqkx5iiNYMW2Qkor3MCFVz6o00pERFqKgGt0UlNT2bBhAx9//DHbt28HoF+/fowbNy7ok5PG4dtW3tM4TIa5mwrb5H33SADat41k3h0DVIQsIiJhr153XRmGwfjx4xk/fnyw5yONrHpb+aTK1ZxV1gCOkgBAdITJ+PSUEM1QREQkeALeunr44Yd58cUXL3i+cOFCHnnkkaBMShqPf1u5zWTTc+XDu+4x3jGFThdr84+HYHYiIiLBFXDQ+ctf/sKoUaMueD5y5Ej+/Oc/B2VS0nh828qHGDtINYs5bbfhH1ZmreNERETCVcBB59ixYyQkJFzwPD4+nqNHjwZlUtJ4fNvF76jctsp2D6WU6FrHiYiIhKuAg07v3r3Jzs6+4Pnf//53evbsGZRJSeM5UeLCNCCKcm51fA7Au9b5s3PUVi4iIi1JwMXIWVlZzJw5k+LiYm644QYAcnJyeP7551mwYEHQJyjBk51bwINvb8QGxpobSTDOUmAn8rmV7jdObeUiItJSBBx0vve97+FyufjlL3/JU089BUBaWhovv/wyU6dODfoEJTiqd1tVbVu95x6FVbmwZxqw8LuD1VYuIiItRr3ay2fMmMGMGTMoLi6mTZs2xMXFBXteEmS+3VbtOc1YcyMA77rPF5ZbNnSIjQrJ/ERERBpDwDU6ABUVFXz88ccsW7YM2/asERw+fJgzZ84EdXISPL5dVLc6viDKcLPN6s4O+/Jax4mIiIS7gFd09u3bx80338z+/ftxuVyMHz+edu3a8eyzz+JyuVi8eHFjzFMayLeLqurKh2XVLvCsPk5ERCTcBbyiM2vWLIYMGcKJEydo06aN9/nkyZPJycmp1yQWLVpEWloaMTExDB8+nLVr19Y69tVXX2XMmDF06NCBDh06MG7cuIuOF4+qbqvLjSKGmDtx2wZ/rbzyAdRtJSIiLVPAQWfVqlX87Gc/IyrKv5YjLS2NQ4cOBTyBpUuXkpWVxdy5c9mwYQODBg3ipptu4siRIzWOX7lyJd/97nf55z//yZo1a0hNTWXChAn1+tmtRVW3lWXDpMqTkFdb/TlCB79x6rYSEZGWJuCgY1kWbrf7gucHDx6kXbt2AU/ghRde4P7772f69Omkp6ezePFi2rZty5IlS2oc//vf/54HHniAjIwM+vbty//93/9hWVa9V5NaOv9uK5vJjlXA+ZvKwdNttehudVuJiEjLE3DQmTBhgt95OYZhcObMGebOncstt9wS0PcqKytj/fr1fjefm6bJuHHjWLNmTZ2+x9mzZykvLycxseYtF5fLhdPp9PtoTXy7ra42dtHDLOKsHc1H1lDvGHVbiYhISxVw0Hn++edZvXo16enplJaWcvfdd3u3rZ599tmAvtfRo0dxu90kJyf7PU9OTqawsLBO3+PRRx+lS5cufmHJ17x580hISPB+pKamBjTHcOfbRVV1U/lH1hDOElPrOBERkZYi4K6rbt26sXnzZpYuXcrmzZs5c+YM9913H/fcc49fcXJTeOaZZ3jnnXdYuXIlMTE1dwvNmTOHrKws7+dOp7NVhZ2kOM8dVpFUMNHhWSV7V91WIiLSStTrwMCIiAjuuece7rnnHr/n586dCyjsJCUl4XA4KCoq8nteVFRESkrKRd997rnneOaZZ/j4448ZOHBgreOio6OJjo6u9estWXZuAU/8dSsA15mbSTTOcMRuz2qrv3eMAaSo20pERFqoeh0YWJ3L5eL555+nR48eAb0XFRVFZmamXyFxVWHxiBEjan3vV7/6FU899RTZ2dkMGTKk3vNuybJzC5jx1gYKnS4AbxHyX90jcOMAPCEH1G0lIiItV52DjsvlYs6cOQwZMoSRI0eyfPlyAF5//XV69OjBggULmD17dsATyMrK4tVXX+W3v/0teXl5zJgxg5KSEqZPnw7A1KlTmTNnjnf8s88+y89//nOWLFlCWloahYWFFBYW6lRmH9XvtYqnhHHeKx/GeMelJMTw8r3qthIRkZarzltXjz/+OK+88grjxo3js88+484772T69Ol8/vnnvPDCC9x55504HI6AJzBlyhSKi4t5/PHHKSwsJCMjg+zsbG+B8v79+zHN83ns5ZdfpqysjG9/+9t+32fu3Lk88cQTAf/8lsi30wrgG461RBvl7LC6sdXu7n3+3LcHMapPUiimKCIi0iTqHHT+9Kc/8eabb3LbbbeRm5vLwIEDqaioYPPmzRhGw7Y9Zs6cycyZM2v82sqVK/0+37t3b4N+VmtQvYPqjsptq+Xu0ZzfsIKjJa6mnJaIiEiTq/PW1cGDB8nMzASgf//+REdHM3v27AaHHAk+3w6qrhQz3NyOZRss97mpvPo4ERGRlqjOQcftdvtd+xAREUFcXFyjTEoaZliPRFLiPSHmdofnyofPrX4UcBmge61ERKT1qPPWlW3b/Od//qe3Vbu0tJQf/vCHxMbG+o1btmxZcGcoAVuxrZDSCjdgc0flIYHvWp6zc9RpJSIirUmdg860adP8Pr/33nuDPhlpuKq2chvob+TT2zxMqR3J393DAGjfNpJ5dwxQp5WIiLQKdQ46r7/+emPOQ4Kgelt51WrOCiuTM7QFIDrCZHz6xQ9jFBERaSmCcmCgNA++beUO3Ex0fAbAMp+zcwqdLtbmHw/J/ERERJqagk4L4ttWPsbcQkfDyVE7nlXWgFrHiYiItGQKOi2Ib7v45Mpuq/fdI6iotkOptnIREWkt6nWppzRPJ0pcmAa0sc8xwVwH+N9Urgs8RUSktVHQaSGycwt48O2N2HiufGhjlLHb6swWu6ffOLWVi4hIa6KtqxagerfVJLPy7ByfKx9MAxbdrQs8RUSkdVHQaQF8u61SOMZIcxsAy63zVz5YNnSIjarxfRERkZZKQacF8O2iut3xGaZhs9a6koN2p1rHiYiItAYKOi2AbxfVJIfvtlXt40RERFoDFSO3AFXdVleyj37mAVx2BB+6h3u/rm4rERFprRR0wpxvt9XkCM9qTo41GCf+N8ur20pERFojbV2FMd9uKxOL2ysPCVzuPl+ErG4rERFpzRR0wphvt9VIcyvJxklO2HH807raO0bdViIi0pop6IQx3y6qyY5VAHzgvobyajuS6rYSEZHWSkEnjFV1UbWhlJvNLwF1W4mIiPhS0Aljmd07kBgbxQRzHbGGi71WMhvsPt6vG0BndVuJiEgrpqATprJzC7hu/j85XlLGHZVn53hOQvZ0VlX1V6nbSkREWjO1l4eh7NwCZry1ARvoyAlGm18B/t1WKQkxzJ2Yrm4rERFp1RR0wkz1Czxvc6zBYdhssHqz1/aEmsTYSD7977FERWjBTkREWjf9SRhmfFvKASZXblstc4/xPjteUs76fSeafG4iIiLNjYJOmPFtFe9jHKS/uZdy2+F35UP1cSIiIq2Vgk6Y8W0Vv6Py7JyVVgYniK91nIiISGuloBNmqi7wNHyufFjmc3aOWspFRETOUzFyGPG9wHOEmUcX4zhOuy2f+Fz5AGopFxERqaIVnTBRvdtqsukpQv7QPRwXnrusdIGniIiIPwWdMOHbbRVNGd9wrAX8r3zQBZ4iIiL+FHTChG8X1XhzPe2Mcxy0k/jSvrLWcSIiIq2dgk6Y8O2iqjo7Z7l7FHa1f4TqthIRETlPxchhoqrbqr3t5DpzM+C/bWXgufZB3VYiIiLnKeiEAd9uq4mONUQYFputnuy2u/qNU7eViIiIP21dNXMXdFtVHhLoe4Gnuq1ERERqpqDTzPl2W/U0DpNh7qHCNvmre6R3jLqtREREaqag08z5dlFNqixC/pc1kGMk1DpOREREPBR0mrmkuGjAc+XDZNNz5YNvEXIVdVuJiIhcSMXIzVh2bgFP/HUrAEOMnaSaxZy227DCyvSOUbeViIhI7RR0mqns3AJmvLXBpwjZs22V7R5KKVWrPB7qthIREamZgk4zVL3TKpoybnV8DsAya4x3XEpCDHMnpqvbSkREpBYKOs2Qb6cVwFhzEwnGWQrsRL6w+nmfP/ftQYzqkxSKKYqIiIQFFSM3Q9U7qKq2rd5zj8Ly+Ud2tMTVpPMSEREJNwo6zZBvB1V7TjPW3AjAsmrdVuq0EhERuTgFnWao6l4rgG86PifKcLPN6s5OOxXwFCF3VqeViIjIJYU86CxatIi0tDRiYmIYPnw4a9eurXXs1q1b+da3vkVaWhqGYbBgwYImnGnTqLrXyqqsRK7atqq+mqNOKxERkUsLadBZunQpWVlZzJ07lw0bNjBo0CBuuukmjhw5UuP4s2fP0rNnT5555hlSUlKaeLaNr3q31eVGEZnm17htg/cqr3zQvVYiIiJ1F9Kg88ILL3D//fczffp00tPTWbx4MW3btmXJkiU1jh86dCjz58/nrrvuIjo6uoln2/iqd1tNNj2rOaut/hTTAdC9ViIiIoEIWdApKytj/fr1jBs37vxkTJNx48axZs2aoP0cl8uF0+n0+2iu/LutbO+2VfUrH3SvlYiISN2ELOgcPXoUt9tNcnKy3/Pk5GQKC3gUtbEAABuUSURBVAuD9nPmzZtHQkKC9yM1NTVo3zvYfLuorjZ2kWYWcdaO5iNraK3jREREpHYhL0ZubHPmzOHUqVPejwMHDoR6SrUa1iORlHhPiPFe+WAN5SyeZ+q2EhERCUzITkZOSkrC4XBQVFTk97yoqCiohcbR0dFhU8+zYlshpRVuIqlgosOzfbfcPQrQvVYiIiL1EbIVnaioKDIzM8nJyfE+syyLnJwcRowYEapphUzVJZ4nz5ZznbmZDsYZjtjtWW31B6B920hevlfdViIiIoEI6V1XWVlZTJs2jSFDhjBs2DAWLFhASUkJ06dPB2Dq1Kl07dqVefPmAZ4C5m3btnn//tChQ2zatIm4uDh69+4dst+joaq3lU92rALgPfdI3DgAiI4wGZ/e8lrqRUREGlNIg86UKVMoLi7m8ccfp7CwkIyMDLKzs70Fyvv378c0zy86HT58mKuvvtr7+XPPPcdzzz3Hddddx8qVK5t6+kHj21YeTwnjKq98WO7TbVXodLE2/zgjel0WkjmKiIiEo5DfXj5z5kxmzpxZ49eqh5e0tDRs265xbDjzbRe/xfEF0UY5O6xubLW71zpORERELq3Fd12FA992cf+zc4xax4mIiMilhXxFR85f4tmFYoab27Fsg/cqu63AE3dS1FYuIiISMAWdEKu6xNMGbnesBuBzqx8F+NfiqK1cREQkcNq6CiH/biufKx+s80XIusRTRESk/hR0Qsi322qAkU9v8zCldiR/dw/zjtElniIiIvWnoBNCvl1Ud1SenbPCyuQMbWsdJyIiInWnoBNCSXGeqykifK58WOYec8E4dVuJiIjUj4qRQyQ7t4An/roVgNHmVyQZTo7a8ayyBnjHqNtKRESkYRR0QqDqXquqow/vqCxCft89gorKfyS6xFNERKThFHSaWPV7reI4ywRzHVB1SKBHSkIMcyemq9tKRESkARR0mphvpxXAzY4viTHK2W11Zovd0/v8uW8PYlSfpFBMUUREpMVQMXITq95BNdms+cqHoyWuppyWiIhIi6Sg08R8O6hSOMYIcxsAy30OCaw+TkREROpHQaeJDeuRSEq8J8Tc7vgM07D5wurLQbsj4FnT6axOKxERkaBQ0GliK7YVUlrhxu/Kh8oiZHVaiYiIBJeKkZuQb1t5urGPvuYBXHYEf6u88qF920jm3TFAnVYiIiJBohWdJlK9rXxS5U3lOdZgnMQBEB1hMj49JUQzFBERaXkUdJqIb1u5icXtlUHH9+ycQqeLtfnHQzI/ERGRlkhBp4n4tpWPMnNJNk5ywo5jpZVR6zgRERFpGAWdJuLbLl5VhPyB+xrKq5VJqa1cREQkeFSM3EROlLgwDYj5/+3deVBUd7YH8O/t1mZRoVGQBmVzAaPgxmiLRmNGJmCcRDQZGcIMmjEmcXRixmUcM5lgfFXRFzNJZRKHSU1FtLKRWE/JPCVMuZEYxY2AigsqAUkiixuLioDd5/1h+j6uoGjspqX5fqqowt89ffuc+6PaU/feX1+5hnjdAQDay1Z8gCcREZH9sdFpB9mF5Zj3cT4EwCO6g/BUGlBq9cc3MlATx2XlRERE9sVLVw5282qr6fpdAIBM6zjYvjlHpwBrnhrJZeVERER2xkbHwZqvtvLDJYzTFQLQXrayCuDTzeCU/IiIiFwZGx0Ha76K6nH9HugVwTfWATgjplvGERERkX2w0XGw5quopv+42mqjZfxt44iIiMg+eDOyg9lWWw3AdxiiO4NG0WOzZYy6nautiIiIHIeNjgM1X201rcuNszk51uGoRg9NHFdbEREROQYvXTlI89VWyi0e+cDVVkRERI7FRsdBmq+2GqM7jkDlImrFEzusI9QYrrYiIiJyLDY6DtJ8FdU0ne2RD2Y0wHDLOCIiIrIvNjoO4tvdDQDgjgZM1u8HAGQ2u2xlw9VWREREjsObkR0gu7Acy/99FADwC10eeij1+F58cUAi1BiutiIiInI8Njp2ll1YjrkffqM+8iGh2U3I8uMJNNv6Kq62IiIiciw2OnZ083OteqEGD+kOAQAyLePUOJO3O1IfG8zVVkRERA7GRseOmq+0AoDH9LnoolhxyNoPxdJHHX/jyWEYN9DXGSkSERF1KrwZ2Y5uXkGV8OMjHzbddBPy+SsN7ZYTERFRZ8ZGx46ar6Dqp5zFcN23uC46/K8l5pZxRERE5DhsdOxodFhPmLxuNDHTfjyb85V1KC7AG8CNm5ADuNKKiIio3bDRsaOtxypw7boFCqxqo2O7bMWVVkRERO2PNyPbSfNl5aOUk+irnEedeGCrNRoAYPTsipXTo7jSioiIqB3xjI4d3LysfJp+FwAg2zIK13DjG5Lduujwi8EmJ2VIRETUObHRsYPmy8rd0Ihf6vcBADZax6sxFbUN2F9y0Sn5ERERdVZsdOyg+bLyh3UF8FKu4qz0xF7rA7eMIyIiIsdjo2MHzZeLT//xstW/LePURz60FkdERESOd180OmvWrEFoaCjc3d1hNpuxf//+28Zv2LABgwYNgru7O6KiopCVldVOmbbu0pUG6BTAiDpM1BUAADY2+5JALisnIiJyDqc3Op9++ikWLlyI1NRUfPPNNxg2bBji4uJQVVXVavyePXuQlJSE2bNnIz8/HwkJCUhISEBhYWE7Z35DdmE55n2cD6sAv9TvhUGx4Kg1BCclSBPHZeVERETtTxERaTvMccxmM0aNGoV3330XAGC1WhEUFIQ//OEP+POf/9wiPjExEVeuXMHmzZvVsTFjxmD48OH45z//2eb71dbWwtvbGzU1NfDy8rqn3C1WwYP/vUO9Efl/DKmI1p3CfzUl433LFACATgHeTRqJR4dyWTkREdFP9VP//3bqGZ3Gxkbk5eUhNjZWHdPpdIiNjUVubm6rr8nNzdXEA0BcXNwt4xsaGlBbW6v5sZfmq61ClApE607BIgr+bRmrxlgF8OlmsNt7EhER0Z1zaqNz/vx5WCwW+Pv7a8b9/f1RUVHR6msqKiruKn7lypXw9vZWf4KCglqN+ymar6IKVqpQJUbstkbiHHxuGUdERETtx+n36DjasmXLUFNTo/589913dtt381VUu6xDEdPwDhY1zb1tHBEREbUfpz4CwtfXF3q9HpWVlZrxyspKmEytf4uwyWS6q3g3Nze4ubnZJ+GbjA7riQBvd1TUXIMAsECPczCq2xUAJq62IiIichqnntExGAyIjo7G9u3b1TGr1Yrt27cjJiam1dfExMRo4gFg69att4x3JL1OQepjgwH8/0M7bfgQTyIiIudz+qWrhQsX4l//+hfWr1+P48ePY+7cubhy5QqefvppAEBKSgqWLVumxi9YsADZ2dn429/+hhMnTmD58uU4ePAg5s+f75T84yMDkPabkTB5ay9PmbzdkfabkXyIJxERkRM5/enliYmJOHfuHF555RVUVFRg+PDhyM7OVm84Lisrg073//3Y2LFj8fHHH+Pll1/GSy+9hIEDByIzMxORkZHOKgHxkQH4xWAT9pdcRFXdNfTuceNyFc/kEBEROZfTv0envdnze3SIiIiofXTI79EhIiIiciQ2OkREROSy2OgQERGRy2KjQ0RERC6LjQ4RERG5LDY6RERE5LLY6BAREZHLYqNDRERELouNDhEREbkspz8Cor3Zvgi6trbWyZkQERHRnbL9v323D3TodI1OXV0dACAoKMjJmRAREdHdqqurg7e39x3Hd7pnXVmtVpw9exY9evSAotj3oZu1tbUICgrCd9991ymfo8X6WT/rZ/2sn/U7qn4RQV1dHQIDAzUP+25Lpzujo9Pp0LdvX4e+h5eXV6f8Q7dh/ayf9bP+zor1O7b+uzmTY8ObkYmIiMhlsdEhIiIil6Vfvnz5cmcn4Ur0ej0mTpyILl063VVBAKyf9bN+1s/6Wf/9VX+nuxmZiIiIOg9euiIiIiKXxUaHiIiIXBYbHSIiInJZbHSIiIjIZbHRsZM1a9YgNDQU7u7uMJvN2L9/v7NTatPKlSsxatQo9OjRA71790ZCQgKKioo0MRMnToSiKJqf559/XhNTVlaGKVOmwNPTE71798aSJUtw/fp1TUxOTg5GjhwJNzc3DBgwAOvWrWuRT3sfw+XLl7eobdCgQer2a9euYd68eejVqxe6d++OJ554ApWVlZp9dNTaASA0NLRF/YqiYN68eQBcb+6/+uorPPbYYwgMDISiKMjMzNRsFxG88sorCAgIgIeHB2JjY3Hq1ClNzMWLF5GcnAwvLy8YjUbMnj0bly9f1sQcPnwY48ePh7u7O4KCgvD666+3yGXDhg0YNGgQ3N3dERUVhaysrLvOxZ71NzU1YenSpYiKikK3bt0QGBiIlJQUnD17VrOP1v5mVq1a1eHrB4BZs2a1qC0+Pl4T46rzD6DVzwJFUbB69Wo1psPOv9A9y8jIEIPBIGvXrpWjR4/KnDlzxGg0SmVlpbNTu624uDhJT0+XwsJCKSgokEcffVSCg4Pl8uXLasxDDz0kc+bMkfLycvWnpqZG3X79+nWJjIyU2NhYyc/Pl6ysLPH19ZVly5apMd9++614enrKwoUL5dixY/LOO++IXq+X7OxsNcYZxzA1NVWGDBmiqe3cuXPq9ueff16CgoJk+/btcvDgQRkzZoyMHTvWJWoXEamqqtLUvnXrVgEgO3fuFBHXm/usrCz5y1/+Ihs3bhQAsmnTJs32VatWibe3t2RmZsqhQ4fk8ccfl7CwMKmvr1dj4uPjZdiwYbJ3717ZtWuXDBgwQJKSktTtNTU14u/vL8nJyVJYWCiffPKJeHh4yHvvvafG7N69W/R6vbz++uty7Ngxefnll6Vr165y5MiRu8rFnvVXV1dLbGysfPrpp3LixAnJzc2V0aNHS3R0tGYfISEhsmLFCs3fRPPPi45av4jIzJkzJT4+XlPbxYsXNTGuOv8ioqm7vLxc1q5dK4qiSHFxsRrTUeefjY4djB49WubNm6f+22KxSGBgoKxcudKJWd29qqoqASBffvmlOvbQQw/JggULbvmarKws0el0UlFRoY6lpaWJl5eXNDQ0iIjIn/70JxkyZIjmdYmJiRIXF6f+2xnHMDU1VYYNG9bqturqaunatats2LBBHTt+/LgAkNzcXBHp2LW3ZsGCBdK/f3+xWq0i4tpzf/MHvdVqFZPJJKtXr1bHqqurxc3NTT755BMRETl27JgAkAMHDqgxX3zxhSiKIj/88IOIiPzjH/8QHx8ftX4RkaVLl0pERIT67xkzZsiUKVM0+ZjNZnnuuefuOJd71dp/dDfbv3+/AJAzZ86oYyEhIfLWW2/d8jUduf6ZM2fK1KlTb/mazjb/U6dOlZ///OeasY46/7x0dY8aGxuRl5eH2NhYdUyn0yE2Nha5ublOzOzu1dTUAAB69uypGf/oo4/g6+uLyMhILFu2DFevXlW35ebmIioqCv7+/upYXFwcamtrcfToUTWm+fGxxdiOjzOP4alTpxAYGIh+/fohOTkZZWVlAIC8vDw0NTVpcho0aBCCg4PVnDp67c01Njbiww8/xO9+9zvNw25dee6bKykpQUVFhSYPb29vmM1mzXwbjUb87Gc/U2NiY2Oh0+mwb98+NWbChAkwGAxqTFxcHIqKinDp0iU15nbH5E5yaQ81NTVQFAVGo1EzvmrVKvTq1QsjRozA6tWrNZcqO3r9OTk56N27NyIiIjB37lxcuHBB3daZ5r+yshJbtmzB7NmzW2zriPN/f319YQd0/vx5WCwWzYc9APj7++PEiRNOyuruWa1WvPjiixg3bhwiIyPV8aeeegohISEIDAzE4cOHsXTpUhQVFWHjxo0AgIqKilZrt227XUxtbS3q6+tx6dIlpxxDs9mMdevWISIiAuXl5Xj11Vcxfvx4FBYWoqKiAgaDocWHvL+/f5t12bbdLsbZtd8sMzMT1dXVmDVrljrmynN/M1u+reXRvJbevXtrtnfp0gU9e/bUxISFhbXYh22bj4/PLY9J8320lYujXbt2DUuXLkVSUpLmAY0vvPACRo4ciZ49e2LPnj1YtmwZysvL8eabb6q5d9T64+PjMX36dISFhaG4uBgvvfQSJk+ejNzcXOj1+k41/+vXr0ePHj0wffp0zXhHnX82OgQAmDdvHgoLC/H1119rxp999ln196ioKAQEBGDSpEkoLi5G//792ztNu5o8ebL6+9ChQ2E2mxESEoLPPvsMHh4eTsys/b3//vuYPHkyAgMD1TFXnnu6taamJsyYMQMigrS0NM22hQsXqr8PHToUBoMBzz33HFauXAk3N7f2TtWufv3rX6u/R0VFYejQoejfvz9ycnIwadIkJ2bW/tauXYvk5GS4u7trxjvq/PPS1T3y9fWFXq9vsRqnsrISJpPJSVndnfnz52Pz5s3YuXMn+vbte9tYs9kMADh9+jQAwGQytVq7bdvtYry8vODh4XHfHEOj0Yjw8HCcPn0aJpMJjY2NqK6uvmVOrlL7mTNnsG3bNjzzzDO3jXPlube91+3yMJlMqKqq0my/fv06Ll68aJe/iebb28rFUWxNzpkzZ7B161bN2ZzWmM1mXL9+HaWlpQA6fv3N9evXD76+vpq/d1effwDYtWsXioqK2vw8ADrO/LPRuUcGgwHR0dHYvn27Oma1WrF9+3bExMQ4MbO2iQjmz5+PTZs2YceOHS1OObamoKAAABAQEAAAiImJwZEjRzQfALYPyMGDB6sxzY+PLcZ2fO6XY3j58mUUFxcjICAA0dHR6Nq1qyanoqIilJWVqTm5Su3p6eno3bs3pkyZcts4V577sLAwmEwmTR61tbXYt2+fZr6rq6uRl5enxuzYsQNWq1VtAmNiYvDVV1+hqalJjdm6dSsiIiLg4+OjxtzumNxJLo5ga3JOnTqFbdu2oVevXm2+pqCgADqdTr2k05Hrv9n333+PCxcuaP7eXXn+bd5//31ER0dj2LBhbcZ2mPn/Sbcwk0ZGRoa4ubnJunXr5NixY/Lss8+K0WjUrEa5H82dO1e8vb0lJydHs1zw6tWrIiJy+vRpWbFihRw8eFBKSkrk888/l379+smECRPUfdiWGD/yyCNSUFAg2dnZ4ufn1+oS4yVLlsjx48dlzZo1rS4xbu9juGjRIsnJyZGSkhLZvXu3xMbGiq+vr1RVVYnIjeXlwcHBsmPHDjl48KDExMRITEyMS9RuY7FYJDg4WJYuXaoZd8W5r6urk/z8fMnPzxcA8uabb0p+fr66qmjVqlViNBrl888/l8OHD8vUqVNbXV4+YsQI2bdvn3z99dcycOBAzfLi6upq8ff3l9/+9rdSWFgoGRkZ4unp2WJ5bZcuXeSNN96Q48ePS2pqaqvLa9vKxZ71NzY2yuOPPy59+/aVgoICzeeBbQXNnj175K233pKCggIpLi6WDz/8UPz8/CQlJaXD119XVyeLFy+W3NxcKSkpkW3btsnIkSNl4MCBcu3aNXUfrjr/NjU1NeLp6SlpaWktXt+R55+Njp288847EhwcLAaDQUaPHi179+51dkptAtDqT3p6uoiIlJWVyYQJE6Rnz57i5uYmAwYMkCVLlmi+S0VEpLS0VCZPniweHh7i6+srixYtkqamJk3Mzp07Zfjw4WIwGKRfv37qezTX3scwMTFRAgICxGAwSJ8+fSQxMVFOnz6tbq+vr5ff//734uPjI56enjJt2jQpLy/X7KOj1m7zn//8RwBIUVGRZtwV537nzp2t/r3PnDlTRG4sa/3rX/8q/v7+4ubmJpMmTWpxXC5cuCBJSUnSvXt38fLykqefflrq6uo0MYcOHZIHH3xQ3NzcpE+fPrJq1aoWuXz22WcSHh4uBoNBhgwZIlu2bNFsv5Nc7Fl/SUnJLT8PbN+rlJeXJ2azWby9vcXd3V0eeOABee211zSNQEet/+rVq/LII4+In5+fdO3aVUJCQmTOnDktmm1XnX+b9957Tzw8PKS6urrF6zvy/CsiIj/tXBARERHR/Y336BAREZHLYqNDRERELouNDhEREbksNjpERETkstjoEBERkctio0NEREQui40OERERuSw2OkREROSy2OgQkdPk5ORAUZQWD09tD4qiQFEUGI3GO4q35aooChISEhycHRHZCxsdImoXEydOxIsvvqgZGzt2LMrLy+Ht7e2UnNLT03Hy5Mk7irXlOmPGDAdnRUT2xEaHiJzGYDDAZDJBURSnvL/RaFSfvNwWW64eHh4OzoqI7ImNDhE53KxZs/Dll1/i7bffVi//lJaWtrh0tW7dOhiNRmzevBkRERHw9PTEk08+iatXr2L9+vUIDQ2Fj48PXnjhBVgsFnX/DQ0NWLx4Mfr06YNu3brBbDYjJyfnrvM8dOgQHn74YfTo0QNeXl6Ijo7GwYMH7XUYiMgJujg7ASJyfW+//TZOnjyJyMhIrFixAgDg5+eH0tLSFrFXr17F3//+d2RkZKCurg7Tp0/HtGnTYDQakZWVhW+//RZPPPEExo0bh8TERADA/PnzcezYMWRkZCAwMBCbNm1CfHw8jhw5goEDB95xnsnJyRgxYgTS0tKg1+tRUFCArl272uUYEJFzsNEhIofz9vaGwWCAp6cnTCbTbWObmpqQlpaG/v37AwCefPJJfPDBB6isrET37t0xePBgPPzww9i5cycSExNRVlaG9PR0lJWVITAwEACwePFiZGdnIz09Ha+99tod51lWVoYlS5Zg0KBBAHBXTRIR3Z/Y6BDRfcXT01NtcgDA398foaGh6N69u2asqqoKAHDkyBFYLBaEh4dr9tPQ0IBevXrd1XsvXLgQzzzzDD744APExsbiV7/6lSYXIup42OgQ0X3l5ktFiqK0Oma1WgEAly9fhl6vR15eHvR6vSaueXN0J5YvX46nnnoKW7ZswRdffIHU1FRkZGRg2rRpP6ESIrofsNEhonZhMBg0NxDby4gRI2CxWFBVVYXx48ff8/7Cw8MRHh6OP/7xj0hKSkJ6ejobHaIOjKuuiKhdhIaGYt++fSgtLcX58+fVMzL3Kjw8HMnJyUhJScHGjRtRUlKC/fv3Y+XKldiyZcsd76e+vh7z589HTk4Ozpw5g927d+PAgQN44IEH7JInETkHGx0iaheLFy+GXq/H4MGD4efnh7KyMrvtOz09HSkpKVi0aBEiIiKQkJCAAwcOIDg4+I73odfrceHCBaSkpCA8PBwzZszA5MmT8eqrr9otTyJqf4qIiLOTICJqb4qiYNOmTXf9OIdZs2ahuroamZmZDsqMiOyJZ3SIqNNKSkpC37597yh2165d6N69Oz766CMHZ0VE9sQzOkTUKZ0+fRrAjUtWYWFhbcbX19fjhx9+AHBjNVdb3wdERPcHNjpERETksnjpioiIiFwWGx0iIiJyWWx0iIiIyGWx0SEiIiKXxUaHiIiIXBYbHSIiInJZbHSIiIjIZbHRISIiIpf1f8jV6L+5ZoB8AAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fa4c42b3850>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(t_anal, R_anal, \"o\", t_num, R_num)\n",
    "xlabel(\"time [s]\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that the match very well. But if we zoom on the recovery plot close to the water breakthrough time,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ByhdUaaaqYcOGpKenc80115hZk+WsTroiIlK72B1ObpnzWblP77ku3a2fNqBClwJN7S91ap8RprYthQv5xlhQfehyj3GJL7xd5c7rAVZ/f1epT5WuHIqIiFSd2e0Qqtxfyl4C+z8xLvEd/vLieNj1RpDqcg+EaNLhUmr+KSIiYjGfaYdQcArS3jYWNc77zhiz+cENvzR6S7W5tVbdeO6uKoWq3bt307x5c7NqERERqZUsbYfgdMKJrcas1K4PwH7BGK/b1LjpvMc4aBRt/vvWQFUKVdHR+pcsIiICVbuPyZJ2CMU/wM7lxvIxJ7+5ON6iO8TdB7HDIdADIa4Gq1CoatKkCfv37ycsLKxCJ23VqhXr1q2jdevWVSpORESkOqhqKwR/PxuzhsYycUkaNq7cDmHW0NiqLWbs8v1Ro7dU2jvwQ86PBQRDx99A3B+NUCWVUqFQdfbsWT755BNCQ0MrdNIzZ85gt9urVJiIiEh14GqFcOkMk6sVQkVbGbjaIVwaziLdCGflcjjg27XG8jH7PqE0toW2gp7j4MbRUM8L6wHWcBVqqeBXiQUPDx48WG1bLVj9SKaIiFQPZrdCcJ3TtHYIhbmQ/g/jEt+ZgxfH2w4wnuK7fjD4VWxd3+rA6u/vCs1UORwOT9chIiJS7ZjdCgFMaIcAkLXbCFLblkHxOWMsuCF0/T30/COEXVe188sVqaWCiIhIJflMKwQAezHs/dho1Hl0/cXxZu2NdgidR0BwxdfxFfcpVImIiFSSpa0QXPKzfuwttRjyf1zKxuYP7W83nuJrfbN6S3mJQpWIiEglWdIKAYzeUsc3GbNSu/8NjmJjvF44dP+D8RPawtz3lKtSqBIRkVqvsjeHe7UVAsCF87Dzn0ajzswdF8ej441ZqfbDICDInPcSt7kVqkpKSvj73//O4MGDiYiI8FRNIiIiXlPVHlMebYXgkvMtbF4E3yyBwrPGWEAIdLrLuF8qqkvV30OqrEItFX6qbt267Nmzp0Y39rT6kUwREfGO8npMueaVKtpjCkxuhQBGb6lDa4xZqQOrKJ0HaxxjPMHXdSTUNfmyYjVn9fe325f/4uLiSE9Pr9GhSkREaj67w0nSyt1XvBfKiRGsklbuZmBsZIUvBVa5FQLAD9/DN+8ajTq/P3xx/NqBxqzUtQk1qrdUTeJ2V88//elPJCYmMm/ePDZu3Mj27dvL/Lhr/vz5xMTEEBISQnx8PKmpqRU6bunSpdhsNoYPH37Za3v27GHYsGGEhoZSr149evbsybFjx9yuTUREai53ekx5RcZ2WDEZXm4P/33cCFQhodBrEkxOg3v/WeOaddY0bs9U3XPPPQBMmTKldMxms+F0OrHZbG4tT7Ns2TISExNZsGAB8fHxJCcnM3jwYPbt20d4eHi5xx05coSpU6fSp0+fy147dOgQt9xyC+PHjycpKYmGDRuya9cuQkK0KKSIiFzkEz2mSi7AnhXGU3zHv744HtHJWIev010QVM9z7y+mcvueqqNHj/7s6+5cFoyPj6dnz57MmzcPMDq3R0dHM3nyZKZPn37FY+x2O3379mXcuHGsW7eOs2fP8uGHH5a+fs899xAYGMjf/va3CtdxKauvyYqIiOdtPHSG3y38+qr7/WPCTeZc1vupvAzY+iZsfQsKsowxvwCIvcNYPqbVTeotVQlWf3+7PVNl1r1UFy5cYOvWrcyYMaN0zM/Pj4SEBDZu3FjucU8//TTh4eGMHz+edevWlXnN4XDw8ccf89hjjzF48GC++eYb2rRpw4wZM654mdClqKiIoqKi0u28vLwqfDIREfGWqtwc7vUeU04nHN1g3Hi+9yNwlBjj9SOhxzjoPgYaRJrzXmKJSvWpOnToEMnJyezZsweA2NhYHnzwQdq2bVvhc5w+fRq73X5Za4aIiAj27t17xWPWr1/PokWLSE9Pv+Lr2dnZFBQU8Pzzz/Pss88yZ84cUlJS+PWvf83atWu59dZbr3jc7NmzSUpKqnDtIiJivaq2QvBaj6miAtjxHqT+H2Tvujje+mbjxvN2t4N/YNXeQ3yC2zeqf/rpp8TGxpKamkrnzp3p3LkzmzZtokOHDqxatcoTNQKQn5/PqFGjWLhwIWFhYVfcx7Xw8x133MHDDz9M165dmT59OrfffjsLFiwo99wzZswgNze39Of48eMe+QwiImIOVyuES280z8wtZOKSNFJ2ZlToPK4eU5GhZe+7jQwNcaudwhWdPgifTIe5sfDRw0agCqwL3cfCxA0w9j/Q4U4FqhrE7Zmq6dOn8/DDD/P8889fNj5t2jQGDhxYofOEhYXh7+9PVlZWmfGsrCwiIy+f/jx06BBHjhxh6NChpWOuEBUQEMC+ffuIjo4mICCA2NjYMse2b9+e9evXU57g4GCCg4MrVLeIiFjL7FYIQzpGMTA20pweUw47HPivceP5oTUXx5u0/bG31O+hTiP3zyvVgtuhas+ePbz33nuXjY8bN47k5OQKnycoKIju3buzZs2a0vudHA4Ha9asYdKkSZft365dO3bs2FFm7IknniA/P59XXnmF6OhogoKC6NmzJ/v27Suz3/79+9VXS0SkhnCnFUJFbzCvco+p8zmQ9g5sWQRnXS18bHD9EOMpvmsGgJ/bF4ekmnE7VDVr1oz09HSuu+66MuPp6ek/2wbhShITExkzZgw9evQgLi6O5ORkzp07x9ixYwEYPXo0LVq0YPbs2YSEhNCxY8cyxzdqZKT9n44/+uijjBgxgr59+9K/f39SUlJYuXIln3/+ubsfVUREfJBPtEJwOfmNca/Uzn9CyY/vV6cx3DgKeo43up9LreF2qJowYQL33Xcf3377Lb179wbgq6++Ys6cOSQmJrp1rhEjRnDq1ClmzpxJZmYmXbt2JSUlpfTm9WPHjuHnZrK/8847WbBgAbNnz2bKlCnccMMN/Otf/+KWW25x6zwiIuKbwhtUrO9gRfdzW0kR7P638RTfd5svjkd1MRY17vgbCKzjmfcWn+Z2nyqn00lycjIvv/wyJ0+eBKB58+Y8+uijTJkyBVsN6KthdZ8LEREpn93h5JY5n121FcL6aQOq/uRemTcugW1/h7WzId/4/sMv0LjZPO4+aNlDvaUsZvX3t9uh6qfy8/MBaNCggWkF+QKr/1BERGqDqvSYcj39B1duhVDlJ/d+yumEff+B1Ulw+sd7dhs0h57joNsYqO/erS/iOVZ/f7t9+W/AgAEsX76cRo0alQlTeXl5DB8+nM8++8zUAkVEpOapao8pVyuES88R6cY5KuTY17Bq1sUlZOo0gb6PGvdLBeipcSnL7ZkqPz8/MjMzL7spPTs7mxYtWlBcXGxqgVawOumKiNRkrlmmS798KjPLVJXZrp+VvRfWPA37Pja2A+pArwfg5inGIsfik6z+/q7wTNX27dtLf9+9ezeZmZml23a7nZSUFFq0aGFudSIiUqOY3WOqyq0QLpV3EtY+B+nvgtMBNn/oNgpunQ4NTZr9khqrwqGqa9eu2Gw2bDYbAwYMuOz1OnXq8Nprr5lanIiI1Cye6DFlih/OwlfJ8PXrF1sjtLsdbpsFza73Xh1SrVU4VB0+fBin08k111xDamoqzZo1K30tKCiI8PBw/P39PVKkiIjUDD7VYwqguBA2/x+sewl++N4Ya9ULBj4N0XHeqUFqjAqHKldHctfSMCIiIu6yvMeUi8MO29+DtX+B3B/Xe23WDhKeMrqgqzWCVILbT//Nnj2biIgIxo0bV2Z88eLFnDp1imnTpplWnIiI1CxxbZoQFRpy1R5TcW2aeKYApxMOrobVT0HWTmOsQXPo/2djXT4/XXGRynN7IaI33niDdu3aXTbeoUMHFixYYEpRIiLiu+wOJxsPneHf6SfYeOgMdkfFHyL397Mxa6ix6P2lc0Gu7VlDY81t2ulyYiu8PRTe/a0RqIJDISEJpqQZN6MrUEkVuT1TlZmZSVTU5U9ANGvWjIyMDFOKEhER31TV/lLgxR5TLmcOGe0Rdn9obPsHQ/x9cEsi1PXQjJjUSm6HqujoaL766ivatGlTZvyrr76iefPmphUmIiK+pbz+Upm5hUxckuZWf6khHaMYGBvpmR5TLgXZ8MUc2PoWOEoAm3GJr98MaBRt3vuI/KhSCyo/9NBDFBcXl7ZWWLNmDY899hiPPPKI6QWKiIj1zO4vBR7oMeVSlA8bXoMN86D4nDF23WBImAURHcx/P5EfuR2qHn30Uc6cOcOf/vQnLly4AEBISAjTpk1jxowZphcoIiLW89n+Uj9VcsGYlfpiDpw/bYy16G60R4i5xZqapFZxO1TZbDbmzJnDk08+yZ49e6hTpw7XXXcdwcFaA0lEpKbyuf5SP+VwwK7l8Nkz8P0RY6xJW2Nmqv0wtUcQr3E7VLnUr1+fnj17mlmLiIj4KJ/pL3Wpbz83FjzOSDe264VDv+nQbTT4B3q3Fqn1KhWqtmzZwnvvvcexY8dKLwG6LF++3JTCRETEd1jeX+pSGduNXlOH1hjbQQ3g5gfhpokQXN87NYhcwu0+VUuXLqV3797s2bOHDz74gOLiYnbt2sVnn31GaKhW7hYRqYks7S/1U98fhX9NgDf6GIHKLxDi74cH0+HWRxWoxFJuh6rnnnuO//3f/2XlypUEBQXxyiuvsHfvXu6++25atWrliRpFRMQEVWnaCRf7S0WGlr3EFxka4lY7hUo5dwZSZsC8HrDjPWOs429hUir8Yg7UC/Pce4tUkM3pdLr1X1W9evXYtWsXMTExNG3alM8//5xOnTqxZ88eBgwYUCMagObl5REaGkpubi4NGza0uhwRkSozo2mni93h9Gx/qZ+6cA6+/n/w1atQlGeMXdPP6ITevKtn3lOqLau/v92+p6px48bk5+cD0KJFC3bu3EmnTp04e/Ys58+fN71AERGpGjObdoIH+0v9lL0EvvkbfP48FGQaY5GdYWAStB3g2fcWqSS3Q1Xfvn1ZtWoVnTp14q677uLBBx/ks88+Y9WqVdx2222eqFFERCrJE007PcrphL0fweokOHPAGGvUCgbMhI6/AT+371oR8Rq3Q9W8efMoLDSmjx9//HECAwPZsGEDv/nNb3jiiSdML1BERCqvWjTtdDm6AVbNhO82G9t1m0Lfx6DHWAhQL0TxfRUKVYmJiTzzzDPUq1ePnTt30rt3bwD8/PyYPn26RwsUEZHK8+mmnaVvvseYmdr/ibEdWBd6PQC9p0CI7muV6qNC86ivvfYaBQUFAPTv35+cnByPFiUiIubw2aadALnfwYcPwOu9jUBl84ce42DKNzDgCQUqqXYqNFMVExPDq6++yqBBg3A6nWzcuJHGjRtfcd++ffuaWqCIiFSezzXtBPjhe1j/v7DpDSj5cYas/TC4bSaEXee9OkRMVqGWCh9++CH3338/2dnZ2Gw2yjvEZrNht9tNL9LbrH4kU0TkUlVpY+B6+g8oE6xcR3u8x5RLcSGk/hXWvQyFZ42x1jcb7RGiteyZVJ3V399u9akqKCigYcOG7Nu3j/Dw8CvuUxO6qlv9hyIi8lNm9Jgys0+V2xx22LYU1j4Hed8ZY+GxkPAUXDdICx6Laaz+/na7+ecXX3zBzTffTEBApddi9nlW/6GIiLiU12OqMrNMXm3aCUZ7hAP/Ndboy95tjDVsAf0fhy73gJ+/595baiWrv7/dTka33nqrJ+oQEZFLmN1jyitNO12Ob4bVs+DoV8Z2SCPo8wjETYDAOt6pQcTLau50k4hINVeteky5nD4Aa56GPSuMbf9guOl+uOVhqHPlB5xEagqFKhERH1Uteky55GfCF3Ng69vgtIPND7r8HvrPgNCWVlcn4hUKVSIiPsqne0y5FObBhldh43wo/nH91+t/YbRHiIi1ri4RC7i9iNKbb76phZNFRLzA1WOqvLulbBhP8Hm1x5RLSRF8vQBe7QpfvmgEqpY94Q//gd8vVaCSWsntUDV9+nQiIyMZP348GzZs8ERNIiKCcWP5rKFGOLk0WLm2Zw2N9e5CyA4HbH8f5vWElGlw/gw0vRYk38MzAAAgAElEQVTu/huMXwUxN3uvFhEf43aoOnHiBG+//TanT5+mX79+tGvXjjlz5pCZmemJ+kREqjW7w8nGQ2f4d/oJNh46g93hVhcbhnSM4vV7uxEZWvYSX2RoiPeadroc+gz+eiss/yOcPQr1I+D2ZPjTJogdpn5TUuu53afqp7KysliyZAlvv/02e/fuZciQIYwfP56hQ4fi5+d2XvMZVve5EJGawcyGm17vMfVTJ9ONXlPfrjW2gxrALQ/CTX+CoHreqUGkAqz+/q5SqALYtGkTixcv5u233yYqKorvv/+exo0b8+abb9KvXz+TyvQuq/9QRKT6M7Npp2VyDsNnz8LOfxrbfoFGn6k+U6Gej7RwEPkJq7+/KzWdlJWVxUsvvUSHDh3o168feXl5fPTRRxw+fJgTJ05w9913M2bMGLNrFRGpFq7WtBOMpp3uXgr0mnOn4ZNpxn1TrkDV6W6YvAWGzFagEimH2y0Vhg4dyqeffsr111/PhAkTGD16NE2aXHzypF69ejzyyCO8+OKLphYqIlJdVMumnQBFBfD1/4OvXoUL+cZY2wHGGn1RXaysTKRacDtUhYeH88UXX9CrV69y92nWrBmHDx+uUmEiItVVtWraCWAvhrR34PPn4Vy2MRbVBRKSoG1/a2sTqUbcClXFxcUcOXKEsLCwn93PZrPRunXrKhUmIlJdVYumnWAseLxnhbGszJmDxljjGBjwJHT4NVTjB45ErOBWqAoMDGT79u2eqkVEpEZwNe3MzC284n1VNoyWCJY07XQ5sh5WzYQTW43tumFw6zTo/gcICLKuLpFqzO2/htx7770sWrTIE7WIiNQIPtm00yVrF7x7N7z1KyNQBdYzwtSUbyD+PgUqkSpw+56qkpISFi9ezOrVq+nevTv16pXtUTJ37lzTihMRsVJVekO5mnZe2qcqspJ9qqrs7HFY+xxs+wfgBJu/MSt16zRoEOHdWkRqKLdD1c6dO+nWrRsA+/fvL/OaTd10RaSGMKNx55COUQyMjbSuaSfA+RxYPxc2/RXsRcZY7HDjvqmwa71Xh0gtUOXmnzWR1c3DRMRaNaJxZ/EPsOkNI1AV5hpjrW+BgU9Dy+7W1ibiIVZ/f7s9U+Vy8OBBDh06RN++falTpw5Op1MzVSJS7V2tcacNo3HnwNhIa+6JuhqHHdL/blzqyz9pjIV3gIFJcG2C1ucT8SC3Q9WZM2e4++67Wbt2LTabjQMHDnDNNdcwfvx4GjduzMsvv+yJOkVEvKLaNu50OmF/irFG36m9xlhoNPR/HDrfDX7+lpYnUhu4/fTfww8/TGBgIMeOHaNu3bql4yNGjCAlJcXU4kREvK3aNe4EOLYJ3vwF/OMeI1CFNIJBz8KkLdD1dwpUIl7i9kzVf//7Xz799FNatmxZZvy6667j6NGjphUmImKFatO4E+DUfliTBHs/MrYDQuCmiXDzQ1CnkbW1idRCboeqc+fOlZmhcsnJySE4ONiUokRErFItGnfmZcAXz0Pa38BpB5sfdB0J/WZAaAvr6hKp5dy+/NenTx/eeeed0m2bzYbD4eCFF16gf3+tESUi1ZtPN+4szDWWlHn1Rtj6lhGobvglTNwId8xToBKxmNszVS+88AK33XYbW7Zs4cKFCzz22GPs2rWLnJwcvvrqK0/UKCLilqo07QQfbNxZUgSbF8GXL8IPOcZYdLyx4HHr8he3FxHvqlSfqtzcXObNm8e2bdsoKCigW7duPPDAA0RF+Xjflgqyus+FiFSeGU07XaoazqrM4YAd78Nnz0LuMWMs7Hq4bRa0+5XaI4hcwurvbzX/vAKr/1BEpHJqRNNOMNojHFoDq56CrB3GWIMo456priPBv9ItBkVqNKu/v92+p+raa6/lqaee4sCBA56oR0SkUq7WtBOMpp12h4//PfJEGrwzDJb8xghUwQ3htpkwOQ26j1GgEvFhboeqBx54gI8//pgbbriBnj178sorr5CZmemJ2kREKsydpp0+6cwheH8sLOwPh78E/yC46QF4cBv0eQSCLn/qWkR8S6Waf27evJm9e/fyy1/+kvnz5xMdHc2gQYPKPBUoIuJN1bJpJ0DBKfh4KsyPg13LARt0vsdo3DnkOahrYesGEXGL26HK5frrrycpKYn9+/ezbt06Tp06xdixY82sTUSkwqpV006Aonz4/Hl4tStsXgiOEmNtvvvXwa/fgMatra5QRNxUpYvzqamp/P3vf2fZsmXk5eVx1113mVWXiIhbqkXTTgB7sdFj6os5cO6UMdb8RqM9wjW3WlqaiFSN26Fq//79vPvuu/zjH//g8OHDDBgwgDlz5vDrX/+a+vXre6JGEZGrcjXtnLgkDRuUCVaWN+0E44m+3R8azTtzvjXGGrcxbkKPHQ5+lb5wICI+wu2WCn5+fvTs2ZPf//733HPPPURERHiqNstY/UimSG1lRl8oM/tUmebwl7BqFpxMM7brNYNbp0G3MRAQZE1NIjWQ1d/fbs9U7du3j+uuu84TtYhILWZWGBrSMYqBsZHWNu10ydwBq5+Cg6uN7cB6cPMU6PUABDfwfj0i4lFuzze7AtXWrVtZsmQJS5YsIS0trUpFzJ8/n5iYGEJCQoiPjyc1NbVCxy1duhSbzcbw4cPL3ef+++/HZrORnJxcpRpFxHNcTTsvbYmQmVvIxCVppOzMcOt8/n42erVtyh1dW9CrbVPvB6rvj8Ly/4EFfYxA5RcAPSfAg+nQb7oClUgN5fZMVXZ2NiNGjOCLL76gUaNGAJw9e5b+/fuzdOlSmjVr5tb5li1bRmJiIgsWLCA+Pp7k5GQGDx7Mvn37CA8PL/e4I0eOMHXqVPr06VPuPh988AFff/01zZs3d6smEfGeqzXttGE07RwYG2nd/VAVdT4H1r0MqX8F+wVjrMOdMOBJaNrW2tpExOPcnqmaPHkyBQUFpYso5+TksHPnTvLy8pgyZYrbBcydO5cJEyYwduxYYmNjWbBgAXXr1mXx4sXlHmO32xk5ciRJSUlcc801V9znxIkTTJ48mXfffZfAwEC36xIR76j2TTsBLpw3wtQrXWDjPCNQxfSBCZ/BXW8pUInUEm7PVKWkpLB69Wrat29fOhYbG8v8+fMZNGiQW+e6cOECW7duZcaMGaVjfn5+JCQksHHjxnKPe/rppwkPD2f8+PGsW7fustcdDgejRo3i0UcfpUOHDleto6ioiKKiotLtvLw8tz6HiFRetW3aCWAvgfR34fPZkP/jJcqITjDwKWh7mxY8Fqll3A5VDofjijM/gYGBOBwOt851+vRp7Hb7ZU8QRkREsHfv3ises379ehYtWkR6enq5550zZw4BAQEVnjmbPXs2SUlJFS9cRExT7Zp2gtEeYd9/YHUSnN5njIW2ggFPQKe71B5BpJZy+7/8AQMG8OCDD3Ly5MnSsRMnTvDwww9z2223mVrcpfLz8xk1ahQLFy4kLCzsivts3bqVV155hbfeegtbBf+WOGPGDHJzc0t/jh8/bmbZIvIzXE07y/uv1YbxFKDlTTtdjn0NiwfD0t8bgapOYxj8HEzeAl1GKFCJ1GJuz1TNmzePYcOGERMTQ3R0NADHjx+nY8eOLFmyxK1zhYWF4e/vT1ZWVpnxrKwsIiMjL9v/0KFDHDlyhKFDh5aOuWbHAgIC2LdvH+vWrSM7O5tWrVqV7mO323nkkUdITk7myJEjl503ODiY4OBgt2oXEXP4fNNOl+y9sCbJmKECCKgDN02EWx6CkFBraxMRn+B2808Ap9PJ6tWrSy/RtW/fnoSEhEoVEB8fT1xcHK+99hpghKRWrVoxadIkpk+fXmbfwsJCDh48WGbsiSeeID8/n1deeYXrr7+e/Px8MjLKPn49ePBgRo0axdixY7nhhhuuWpPVzcNEaiOfbNoJkHcS1j5n3DvldIDND24cZbRGaKgni0V8idXf35Va+89mszFw4EAGDhxY5QISExMZM2YMPXr0IC4ujuTkZM6dO1e6OPPo0aNp0aIFs2fPJiQkhI4dO5Y53tXWwTXetGlTmjZtWmafwMBAIiMjKxSoRKRyqtoN3aeadgL8cBa+SoavX4eSH4Neu9uNZWWa6f8lInI5t0PVlClTuPbaay+7CXzevHkcPHjQ7SabI0aM4NSpU8ycOZPMzEy6du1KSkpK6c3rx44dw0/3KIj4NLNmmVxNOy1VXAibF8KXL0HhWWMs+iYY+DS0ire2NhHxaW5f/mvRogUrVqyge/fuZcbT0tIYNmwY3333nakFWsHq6UOR6sTVDf3S/5G45pdev7ebtZfvKsphh+3vwdq/QO6PD6uE3QAJT8ENv1B7BJFqwOrvb7dnqs6cOUNo6OU3ZTZs2JDTp0+bUpSIVA81pht6xnZYMQkythnbDZpD/z9Dl9+Bf6XukhCRWsjt62rXXnstKSkpl41/8skn5XY3F5Gaqdp3Qy8uhDVPw1/7GYEqONSYmZq8FbqNUqASEbe4/X+MxMREJk2axKlTpxgwYAAAa9as4eWXX9aixSK1TLXuhn7sa/j3JDhzwNiOvQN+8SI0iPj540REyuF2qBo3bhxFRUX85S9/4ZlnngEgJiaG119/ndGjR5teoIj4rmrZDb0o35idSl0IOKF+BPzyJYgdZnVlIlLNVapPlcupU6eoU6cO9evXN7Mmy1l9o5tIdWF3OLllzmdk5hZe8b4qGxAZGsL6aQN8456qA6vho4cu3oh+470w6FmjK7qIVHtWf39XqldBSUkJq1evZvny5bgy2cmTJykoKDC1OBHxba5u6MBly8z4VDf08znwwf3w7m+MQNWoFYz6EO6Yr0AlIqZx+/Lf0aNHGTJkCMeOHaOoqIiBAwfSoEED5syZQ1FREQsWLPBEnSLio4Z0jOL1e7td1qcq0he6oTudsPtD+M+jcO4UYDOWlun/OATXrBl2EbGe26HqwQcfpEePHmzbtq1M5/I777yTCRMmmFqciFQPPtcNHSAvA/4zFfZ+ZGw3awfDXoPoOOtqEpEaze1QtW7dOjZs2EBQUFCZ8ZiYGE6cOGFaYSLiHVVdXsbFJ7qhgzE79c3f4NMnoCgX/AKgzyPGT4AWThcRz3E7VDkcDux2+2Xj3333HQ0aNDClKBHxDp9dxLiycg7Dyilw+Etju/mNMGweRHb8+eNEREzg9o3qgwYNKtOPymazUVBQwKxZs/jlL39panEi4jmu5WUubd6ZmVvIxCVppOzMsKiySnDYYeN8eL23EagCQmDgMzB+tQKViHiN2y0VvvvuOwYPHozT6eTAgQP06NGDAwcOEBYWxpdffkl4eLinavUaqx/JFPE0VyuE8rqh+1wrhJ+TtRtWTIYTW4ztmD4w9BVo2tbaukTE66z+/nb78l/Lli3Ztm0by5YtY9u2bRQUFDB+/HhGjhxJnTp1PFGjiJjMneVlfOI+qSspuQDr58KXL4GjGIIbwqBn4MbR4FepbjEiIlVSqYWtAgICGDlyJCNHjiwz/sMPPyhYiVQD1Xp5GYDvthoLIGfvNrav/wXcPhcaNre2LhGp1Uz561xRUREvv/wybdq0MeN0IuJh1XJ5GYAL5+HTx2FRghGo6jaF3yyC3/1DgUpELFfhUFVUVMSMGTPo0aMHvXv35sMPPwTgzTffpE2bNiQnJ/Pwww97rFARMU9cmyZEhYZc1gXdxYbxFGBcmybeLOvnffsFvN4LNs4DpwM63Q0PbIZOvwWbj9/3JSK1QoUv/82cOZM33niDhIQENmzYwF133cXYsWP5+uuvmTt3LnfddRf+/v6erFVETOJaXmbikjRsUGbdPp9aXgbgh7Ow6klIe8fYbtgCbk+G6wdZW5eIyCUqHKref/993nnnHYYNG8bOnTvp3LkzJSUlbNu2DZv+lihS7fj08jIue/8DHydC/o/tHXqMh4SnIERP5YqI76lwS4WgoCAOHz5MixYtAKhTpw6pqal06tTJowVawepHMkW8yayO6qYqOAWfPAa7lhvbTdoaS8zE3GxtXSLi06z+/q7wTJXdbi+zNE1AQAD162tBUpHqzmeWlwFjiZnt70HKNPjhe7D5Q+/J0G86BOrJYhHxbRUOVU6nkz/84Q8EBxtrZxUWFnL//fdTr169MvstX77c3ApFpHY4exw+ehgOrjK2IzsZS8w072ptXSIiFVThUDVmzJgy2/fee6/pxYhILeRwwJZFsPopuFAA/kFw6zS4+UHwD7S6OhGRCqtwqHrzzTc9WYeI1EanDxhLzBzbaGxHxxuzU82ut7YuEZFKqFRHdRGRKrEXw4bX4PPnwV4EgfWMp/p6/lFLzIhItaVQJSLelbEN/j0JMrcb221vg6HJ0KiVtXWJiFSRQpWIeEdxIXwxB756BZx2CGkEQ56HLveoI7qI1AgKVSLieUc3GgsgnzlobMcOh1++CPXDra1LRMREClUi4jlF+bA6CTYvNLbrR8CvXob2Q62tS0TEAxSqRMQzDqyClQ9B3nfG9o2jYNAzUKextXWJiHiIQpWImOt8DqTMgO1Lje1GrWHYq3BNPyurEhHxOIUqETGH0wm7PoD/PArnTwM2uOlPMOBxCKp31cNFRKo7hSoRqbq8DPj4Edj3sbHdrJ3RxDO6p7V1iYh4kUKViFSe0wnp70LKn6EoF/wCoc8j0CcRAoKtrk5ExKsUqkSkcop/MGan0t81tpt3gzvmQUQHa+sSEbGIQpWIuO/7o/DeKKM7us0P+j8OtzwMfv5WVyYiYhmFKhFxz8E18K/x8MP3ULcp/HaxnuwTEUGhSkQqyuGA9S/DZ38BnMblvrvfgUbRVlcmIuITFKpE5OoKc+GDiRef7us2Bn7xAgSGWFuXiIgPUagSkZ+XtRuW3Qs5h8A/GH71EnQbbXVVIiI+R6FKRMq381/w70lQfB5Co43LfS26WV2ViIhPUqgSkcvZi2HVLPh6vrF9TT/4zWKo19TKqkREfJpClYiUVZAN7/8Bjn5lbN/yMAx4Uu0SRESuQqFKRC46ngrvjYb8DAhqAHe+Du2HWl2ViEi1oFAlIsZyM5v/D1JmgKMYwm6AEUug2fVWVyYiUm0oVInUdsU/wEcPw7Z/GNuxw+GO+RBc39q6RESqGYUqkdrs+yNGu4TMHWDzh4FJ0GsS2GxWVyYiUu0oVInUVgdWG8vNFJ6FumFw15vQpq/VVYmIVFsKVSK1jcMB616Ctc8BTmjRHe7+G4S2sLoyEZFqTaFKpDaxl8CH98OO943t7mPhF3MgINjaukREagCFKpFqzO5wkno4h+z8QsIbhBDXpgn+fuXcD2UvhuUTYNcH4BcAQ1+BG+/1bsEiIjWYQpVINZWyM4OklbvJyC0sHYsKDWHW0FiGdIwqu7O9GP45DvasAL9AY7mZdr/0csUiIjWbn9UFiIj7UnZmMHFJWplABZCZW8jEJWmk7My4OFhyweiQvmcF+AcZ/acUqERETKdQJVLN2B1OklbuxnmF11xjSSt3Y3c4oaTI6JC+9yPwD4Z7/g43DPFmuSIitYZClUg1k3o457IZqp9yAhm5hWw+mGH0oNr/CQSEwO/+AdcN9F6hIiK1jO6pEqlmsvPLD1QuwVygzeoJkL0eAuoYgaptfy9UJyJSeylUiVQz4Q1Cfvb1YC6wMPBlIrJ3QGBd+P0yNfUUEfECXf4TqWbi2jQhKjSEKzVOCKGIxYEv0td/B87AejDynwpUIiJeolAlUs34+9mYNTQWoEywCqGINwNf5Gb/XZQE1MV2778g5mZrihQRqYUUqkSqoSEdo3j93m5EhrouBTp5PnAhvfx3UxJQj4Ax/4bWvSytUUSkttE9VSLV1JCOUQyMjST1cA71v/krnXZuwOkXQMC970F0nNXliYjUOgpVItWYv5+NXv57YNeLANgG/QVibrG4KhGR2kmX/0Sqs9wTRrd0px06j4D4/7G6IhGRWkuhSqS6cnVLP3cKIjvB7clgK2cxZRER8TifCFXz588nJiaGkJAQ4uPjSU1NrdBxS5cuxWazMXz48NKx4uJipk2bRqdOnahXrx7Nmzdn9OjRnDx50lPli1jjk8fgxBYIaWSs5xdU1+qKRERqNctD1bJly0hMTGTWrFmkpaXRpUsXBg8eTHZ29s8ed+TIEaZOnUqfPn3KjJ8/f560tDSefPJJ0tLSWL58Ofv27WPYsGGe/Bgi3rX1bdj6FmCD3y6CxjEWFyQiIjan03mldVm9Jj4+np49ezJv3jwAHA4H0dHRTJ48menTp1/xGLvdTt++fRk3bhzr1q3j7NmzfPjhh+W+x+bNm4mLi+Po0aO0atXqqjXl5eURGhpKbm4uDRs2rNwHE/GUrN3w11vBfgEGPAl9p1pdkYiIT7D6+9vSmaoLFy6wdetWEhISSsf8/PxISEhg48aN5R739NNPEx4ezvjx4yv0Prm5udhsNho1anTF14uKisjLyyvzI+KTHA746CEjUF03GPo8YnVFIiLyI0tD1enTp7Hb7URERJQZj4iIIDMz84rHrF+/nkWLFrFw4cIKvUdhYSHTpk3jd7/7Xbmpdfbs2YSGhpb+REdHu/dBRLzlm3fg+CYIqg+3z9WN6SIiPsTye6rckZ+fz6hRo1i4cCFhYWFX3b+4uJi7774bp9PJ66+/Xu5+M2bMIDc3t/Tn+PHjZpYtYo6CU7BqlvF7/8chtKW19YiISBmWNv8MCwvD39+frKysMuNZWVlERkZetv+hQ4c4cuQIQ4cOLR1zOBwABAQEsG/fPtq2bQtcDFRHjx7ls88++9lrq8HBwQQHB5vxkUQ857+PQ+FZiOwMcfdZXY2IiFzC0pmqoKAgunfvzpo1a0rHHA4Ha9asoVevy9cta9euHTt27CA9Pb30Z9iwYfTv35/09PTSy3auQHXgwAFWr15N06ZNvfaZRDzi289h+zLABkOTwV+LIYiI+BrL/8+cmJjImDFj6NGjB3FxcSQnJ3Pu3DnGjh0LwOjRo2nRogWzZ88mJCSEjh07ljnedfO5a7y4uJjf/va3pKWl8dFHH2G320vvz2rSpAlBQUFe/HQiJiguhI8Sjd/jJkCL7tbWIyIiV2R5qBoxYgSnTp1i5syZZGZm0rVrV1JSUkpvXj927Bh+fhWfUDtx4gQrVqwAoGvXrmVeW7t2Lf369TOtdhGv2LwQcg5B/UgY8ITV1YiISDks71Pli6zucyFS6sI5SO4M50/DsHnQbZTVFYmI+Cyrv7+r1dN/IrXO5v8zAlXjGOhyj9XViIjIz1CoEvFVRQXw1SvG730fA/9Aa+sREZGfpVAl4qtS/wrnz0CTa6DzCKurERGRq1CoEvFFRfmw4VXj976PqYWCiEg1oFAl4os2vQE/fA9N2kKnu6yuRkREKkChSsTXXDgHG+cZv986TbNUIiLVhEKViK9J/7sxS9U4Bjr91upqRESkghSqRHyJwwFf/z/j95seAD9/a+sREZEKU6gS8SX7UyDnWwgJha6/t7oaERFxg0KViC/ZON/4Z/exEFzf2lpERMQtClUivuLkN3B0PfgFQNx9VlcjIiJuUqgS8RUbf7yXqsOvIbSFtbWIiIjbFKpEfEHuCdi13Pi91wPW1iIiIpWiUCXiC1L/Co4SiOkDzbtaXY2IiFSCQpWI1Yp/gLS3jd9vmmhtLSIiUmkKVSJW2/G+0eyzUSu4fojV1YiISCVp/QsRC9gdTlIP55Cd9wMJ6/4f9cB44k/NPkVEqi2FKhEvS9mZQdLK3WTkFhJn28MdwXv4gWC+ChlIgtXFiYhIpenyn4gXpezMYOKSNDJyCwEYE/ApAB+U3MyE9w6RsjPDyvJERKQKFKpEvMTucJK0cjfOH7ejOMNgvy0AvG0fBEDSyt3YHc5yziAiIr5MoUrES1IP55TOUAHcG7CKAJuDDfZY9jlb4QQycgtJPZxjXZEiIlJpClUiXpKdfzFQBXOBe/zXAvC2fXC5+4mISPWhUCXiJeENQkp/H+q/kaa2fL5zhrHa0a3c/UREpPpQqBLxkrg2TYgKDcGGkz/4Gzeo/61kIHaMNgo2ICo0hLg2TSysUkREKkuhSsRL/P1szBoaS3fbfjr6HaHQGcgyez/ACFQAs4bG4u9nK/ccIiLiu9SnSsSLhnSMokvbzfAdfGi/mbM0ACAyNIRZQ2MZ0jHK4gpFRKSyFKpEvCnvJFEn/wtA+zse5ZXANoQ3MC75aYZKRKR6U6gS8aYti8FRAq1vpkvPW+hidT0iImIa3VMl4i0lRbD1LeP3uPssLUVERMynUCXiLbs+gHOnoGELaHe71dWIiIjJFKpEvMHphE0LjN97jgd/XXkXEalpFKpEvOG7LXDyG/APhm5/sLoaERHxAIUqEW9IfcP4Z6ffQr2m1tYiIiIeoVAl4mn5mbDrQ+N33aAuIlJjKVSJeNqWN8FRDNE3QfOuVlcjIiIeolAl4kklF2Drm8bv8ZqlEhGpyRSqRDxp97+hIAsaREH7YVZXIyIiHqRQJeJJrjYKPcaBf6C1tYiIiEcpVIl4yomtcGIL+AdB9z9YXY2IiHiYQpWIp2z6q/HPDr+G+uHW1iIiIh6nUCXiCQXZsGu58btuUBcRqRUUqkQ8YetbYL8ALXtCi+5WVyMiIl6gUCViNnsxbFls/B73P9bWIiIiXqNQJWK2PSsgPwPqR0DsHVZXIyIiXqJQJWK2TT+u89d9LAQEWVuLiIh4jUKViJlOpsPxTeAXCD3GWl2NiIh4kUKViJlSXW0UhkODSGtrERERr1KoEjHLudOw45/G77pBXUSk1lGoEjHL1rfAXgTNu0HLHlZXIyIiXqZQJWIGe8nFNgrx/wM2m7X1iIiI1ylUiZhh70eQdwLqNYMOd1pdjYiIWEChSsQMpW0U/gABwZaWIiIi1lCoEqmqzB1wbAP4BUCPcVZXIyIiFlGoEqkq1yxV+2HQsLm1tYiIiGUUqkSq4nwO7Hjf+D1ebRRERGozhSqRqkh7G0oKIbIzRMdbXY2IiGoIakEAABC8SURBVFhIoUqksuwlsHmR8Xv8/WqjICJSywVYXYBIdWN3OEk9nIP/vpXE5R7HWbcpto6/sbosERGxmEKViBtSdmaQtHI3GbmF/CPwDfCHd4puJWLf9wzpGGV1eSIiYiFd/hOpoJSdGUxckkZGbiE32I7Ry383JU4/3jjXn4lL0kjZmWF1iSIiYiGFKpEKsDucJK3cjfPH7TH+/wXgU0cPTtIUgKSVu7E7nOWcQUREajqFKpEKSD2cQ0ZuIQChFHCn/3oA3i4ZDIATyMgtJPVwjlUlioiIxRSqRCogO7+w9Pe7/T+nju0CexytSHW2K3c/ERGpXXwiVM2fP5+YmBhCQkKIj48nNTW1QsctXboUm83G8OHDy4w7nU5mzpxJVFQUderUISEhgQMHDniidKklwhuEAOCHg9H+qwB40z4YsF1xPxERqX0sD1XLli0jMTGRWbNmkZaWRpcuXRg8eDDZ2dk/e9yRI0eYOnUqffr0uey1F154gVdffZUFCxawadMm6tWrx+DBgyks1CyCVE5cmyZEhYaQ4JdGtN8pvnfW59/2m0tftwFRoSHEtWliXZEiImIpy0PV3LlzmTBhAmPHjiU2NpYFCxZQt25dFi9eXO4xdrudkSNHkpSUxP9v795jmrrfP4C/S6EIQ6jKpaBcVWCIeMHJqvMWmzFn3HQ6mZKhu2jcIJOhOFm2oWYZ+9NLDH/sUjZjwndbxC1e+I2gEDVMha0TvOBQWM1GQc0AFUQtz++PhTMrqLiVtuD7lTRpP+dzPv2c8/jIk55bVFSUzTIRwdatW/HBBx/gxRdfREJCAr7++mv8+eef2Lt3b39vDg1SajcVchfEIU39fwCA/1nnoBMaAP/8VpW7IA5qN94AlIjoceXU+1TdunULVVVVyMnJUdrc3NxgMBhQUVFx3/W2bNmCwMBAvPHGGzhy5IjNsvr6elgsFhgMBqXNz88PSUlJqKiowCuvvNJjvM7OTnR2diqfW1tbAQBtbW3/etto8Jnm9QdwpwZ/3XGD8eZ0dKEdABDk64mN82IxLewJ/pshInKi7v+DRZxzJbZTi6orV67AarUiKCjIpj0oKAjnzp3rdZ2jR4/iiy++gMlk6nW5xWJRxrh3zO5l98rLy8PmzZt7tIeGhj50G+hx9bby7hKAJVucNxMiIrJ19epV+Pn5Ofx7B9Qd1a9du4ZXX30Vn332Gfz9/e02bk5ODrKyspTPLS0tCA8Ph9lsdkpQ6B9tbW0IDQ3FpUuX4Ovr6+zpPNYYC9fCeLgOxsJ1tLa2IiwsDMOHO+f8VqcWVf7+/lCr1WhqarJpb2pqgk6n69H/woULaGhowIIFC5S2rq4uAIC7uztqa2uV9ZqamhAc/M9jQ5qamjBx4sRe5+Hp6QlPT88e7X5+fkwQF+Hr68tYuAjGwrUwHq6DsXAdbm7OOWXcqSeqazQaJCYmorS0VGnr6upCaWkp9Hp9j/6xsbGorq6GyWRSXi+88ALmzJkDk8mE0NBQREZGQqfT2YzZ1taG48eP9zomERERkT04/fBfVlYWVqxYgSlTpmDq1KnYunUrbty4gddeew0AkJaWhpEjRyIvLw9DhgxBfHy8zfparRYAbNozMzPx8ccfY+zYsYiMjMSHH36IkJCQHvezIiIiIrIXpxdVKSkpuHz5Mj766CNYLBZMnDgRxcXFyonmZrP5kX/G27BhA27cuIHVq1ejpaUFzzzzDIqLizFkSN9uzOjp6Ync3NxeDwmSYzEWroOxcC2Mh+tgLFyHs2OhEmddd0hEREQ0iDj95p9EREREgwGLKiIiIiI7YFFFREREZAcsqoiIiIjsYFAUVXl5eXjqqacwdOhQBAYGYuHChaitrbXpM3v2bKhUKpvXmjVrbPqYzWbMnz8f3t7eCAwMRHZ2Nu7cuWPTp6ysDJMnT4anpyfGjBmDgoKCHvPZuXMnIiIiMGTIECQlJeHEiRN232ZXlZ+fj4SEBOUmeHq9HgcPHlSW37x5E+np6RgxYgR8fHywePHiHjd/ZRzs52HxYF44x6effgqVSoXMzEyljbnhPL3Fg7nhGJs2beqxn2NjY5XlAy4vZBBITk4Wo9EoNTU1YjKZ5Pnnn5ewsDC5fv260mfWrFmyatUqaWxsVF6tra3K8jt37kh8fLwYDAb55Zdf5MCBA+Lv7y85OTlKn4sXL4q3t7dkZWXJmTNnZMeOHaJWq6W4uFjpU1hYKBqNRr788ks5ffq0rFq1SrRarTQ1NTlmZzjZDz/8IPv375fz589LbW2tvP/+++Lh4SE1NTUiIrJmzRoJDQ2V0tJSqayslKefflqmTZumrM842NfD4sG8cLwTJ05IRESEJCQkyNq1a5V25oZz3C8ezA3HyM3NlXHjxtns58uXLyvLB1peDIqi6l7Nzc0CQMrLy5W2WbNm2STMvQ4cOCBubm5isViUtvz8fPH19ZXOzk4REdmwYYOMGzfOZr2UlBRJTk5WPk+dOlXS09OVz1arVUJCQiQvL+8/b9dANWzYMPn888+lpaVFPDw85Ntvv1WWnT17VgBIRUWFiDAOjtAdDxHmhaNdu3ZNxo4dKyUlJTb7nrnhHPeLhwhzw1Fyc3NlwoQJvS4biHkxKA7/3au1tRUAejxQcffu3fD390d8fDxycnLQ3t6uLKuoqMD48eOVm44CQHJyMtra2nD69Gmlj8FgsBkzOTkZFRUVAIBbt26hqqrKpo+bmxsMBoPS53FitVpRWFiIGzduQK/Xo6qqCrdv37bZP7GxsQgLC1P2D+PQf+6NRzfmheOkp6dj/vz5PfYXc8M57hePbswNx/jtt98QEhKCqKgopKamwmw2AxiYeeH0O6rbW1dXFzIzMzF9+nSbR9csX74c4eHhCAkJwalTp/Dee++htrYWe/bsAQBYLBaboABQPlsslgf2aWtrQ0dHB/766y9YrdZe+5w7d87u2+qqqqurodfrcfPmTfj4+KCoqAhxcXEwmUzQaDTKo4W6BQUFPXQfdy97UB/GoXf3iwfAvHCkwsJC/Pzzzzh58mSPZRaLhbnhYA+KB8DccJSkpCQUFBQgJiYGjY2N2Lx5M2bMmIGampoBmReDrqhKT09HTU0Njh49atO+evVq5f348eMRHByMuXPn4sKFCxg9erSjpzmoxcTEwGQyobW1Fd999x1WrFiB8vJyZ0/rsXW/eMTFxTEvHOTSpUtYu3YtSkpK+vy4LOo/fYkHc8Mx5s2bp7xPSEhAUlISwsPD8c0338DLy8uJM/t3BtXhv4yMDOzbtw+HDx/GqFGjHtg3KSkJAFBXVwcA0Ol0Pa4o6P6s0+ke2MfX1xdeXl7w9/eHWq3utU/3GI8DjUaDMWPGIDExEXl5eZgwYQK2bdsGnU6HW7duoaWlxab/3fuHcbC/+8WjN8yL/lFVVYXm5mZMnjwZ7u7ucHd3R3l5ObZv3w53d3cEBQUxNxzoYfGwWq091mFuOIZWq0V0dDTq6uoG5N+MQVFUiQgyMjJQVFSEQ4cOITIy8qHrmEwmAEBwcDAAQK/Xo7q6Gs3NzUqfkpIS+Pr6KodK9Ho9SktLbcYpKSlRzk/RaDRITEy06dPV1YXS0lKbc1geN11dXejs7ERiYiI8PDxs9k9tbS3MZrOyfxiH/tcdj94wL/rH3LlzUV1dDZPJpLymTJmC1NRU5T1zw3EeFg+1Wt1jHeaGY1y/fh0XLlxAcHDwwPyb8Uintbuot956S/z8/KSsrMzmssz29nYREamrq5MtW7ZIZWWl1NfXy/fffy9RUVEyc+ZMZYzuyzKfffZZMZlMUlxcLAEBAb1elpmdnS1nz56VnTt39npZpqenpxQUFMiZM2dk9erVotVqba5MGMw2btwo5eXlUl9fL6dOnZKNGzeKSqWSH3/8UUT+vjw2LCxMDh06JJWVlaLX60Wv1yvrMw729aB4MC+c696ry5gbznV3PJgbjrNu3TopKyuT+vp6OXbsmBgMBvH395fm5mYRGXh5MSiKKgC9voxGo4iImM1mmTlzpgwfPlw8PT1lzJgxkp2dbXPPERGRhoYGmTdvnnh5eYm/v7+sW7dObt++bdPn8OHDMnHiRNFoNBIVFaV8x9127NghYWFhotFoZOrUqfLTTz/116a7nNdff13Cw8NFo9FIQECAzJ07VymoREQ6Ojrk7bfflmHDhom3t7csWrRIGhsbbcZgHOznQfFgXjjXvUUVc8O57o4Hc8NxUlJSJDg4WDQajYwcOVJSUlKkrq5OWT7Q8kIlIvJov20RERER0b0GxTlVRERERM7GooqIiIjIDlhUEREREdkBiyoiIiIiO2BRRURERGQHLKqIiIiI7IBFFREREZEdsKgiIiIisgMWVUTk0srKyqBSqXo8VNURVCoVVCoVtFptn/p3z1WlUmHhwoX9PDsicjUsqojIZcyePRuZmZk2bdOmTUNjYyP8/PycMiej0Yjz58/3qW/3XJcuXdrPsyIiV8SiiohcmkajgU6ng0qlcsr3a7VaBAYG9qlv91y9vLz6eVZE5IpYVBGRS1i5ciXKy8uxbds25RBaQ0NDj8N/BQUF0Gq12LdvH2JiYuDt7Y0lS5agvb0dX331FSIiIjBs2DC88847sFqtyvidnZ1Yv349Ro4ciSeeeAJJSUkoKyt75Hn++uuvmDNnDoYOHQpfX18kJiaisrLSXruBiAYwd2dPgIgIALZt24bz588jPj4eW7ZsAQAEBASgoaGhR9/29nZs374dhYWFuHbtGl566SUsWrQIWq0WBw4cwMWLF7F48WJMnz4dKSkpAICMjAycOXMGhYWFCAkJQVFREZ577jlUV1dj7NixfZ5namoqJk2ahPz8fKjVaphMJnh4eNhlHxDRwMaiiohcgp+fHzQaDby9vaHT6R7Y9/bt28jPz8fo0aMBAEuWLMGuXbvQ1NQEHx8fxMXFYc6cOTh8+DBSUlJgNpthNBphNpsREhICAFi/fj2Ki4thNBrxySef9HmeZrMZ2dnZiI2NBYBHKsiIaHBjUUVEA463t7dSUAFAUFAQIiIi4OPjY9PW3NwMAKiurobVakV0dLTNOJ2dnRgxYsQjfXdWVhbefPNN7Nq1CwaDAS+//LLNXIjo8cWiiogGnHsPt6lUql7burq6AADXr1+HWq1GVVUV1Gq1Tb+7C7G+2LRpE5YvX479+/fj4MGDyM3NRWFhIRYtWvQvtoSIBhMWVUTkMjQajc3J5fYyadIkWK1WNDc3Y8aMGf95vOjoaERHR+Pdd9/FsmXLYDQaWVQREa/+IyLXERERgePHj6OhoQFXrlxRfmn6r6Kjo5Gamoq0tDTs2bMH9fX1OHHiBPLy8rB///4+j9PR0YGMjAyUlZXh999/x7Fjx3Dy5Ek8+eSTdpknEQ1sLKqIyGWsX78earUacXFxCAgIgNlsttvYRqMRaWlpWLduHWJiYrBw4UKcPHkSYWFhfR5DrVbj6tWrSEtLQ3R0NJYuXYp58+Zh8+bNdpsnEQ1cKhERZ0+CiMgVqVQqFBUVPfIjZ1auXImWlhbs3bu3n2ZGRK6Iv1QRET3AsmXLMGrUqD71PXLkCHx8fLB79+5+nhURuSL+UkVEdB91dXUA/j7sFxkZ+dD+HR0d+OOPPwD8fVXhw+63RUSDC4sqIiIiIjvg4T8iIiIiO2BRRURERGQHLKqIiIiI7IBFFREREZEdsKgiIiIisgMWVURERER2wKKKiIiIyA5YVBERERHZwf8DDW83Qaqy7RoAAAAASUVORK5CYII=",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fa4c40b57d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(t_anal, R_anal, \"o\", t_num, R_num)\n",
    "xlabel(\"time [s]\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "axis([25000, 50000, 0.40, 0.5])\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can see that there is roughly 1 percent underestimation of the recovery factor by the numerical method. One reason is the numerical diffusion in the upwind scheme that I have used in my numerical solution. With this diffusion, the front is not sharp anymore and the water breakthrough (decrease in the slope of the recovery curve from the linear trend) happens a bit earlier in time. Let's test it by plotting the saturation profiles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fa4bb122fd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pv_inj2 = 0.3\n",
    "(t_num, R_num, sw_prf_num)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj2, Nx=50)\n",
    "\n",
    "# Analytical solution (BL)\n",
    "(xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "  muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "  k=perm_ave, swc=swc, sor=sor, kro0=kro0, no=no, \n",
    "  krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj2)\n",
    "visualizeCells(sw_prf_num)\n",
    "plot(xt_prf*t_anal[end], sw_prf)\n",
    "axis([0, L_core, 0, 1.0])\n",
    "legend([\"Numerical\", \"Analytical\"])\n",
    "xlabel(\"Core length [m]\")\n",
    "ylabel(\"Water saturation [-]\")\n",
    "IJulia.clear_output() # only to clear the output from the previous function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see that the extra numerical diffusion causes the water front to move faster resulting in an earlier water breakthrough. We can decrease this diffusion by refining the grid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fa4bb02bb10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(t_num, R_num, sw_prf_num)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj2, Nx=500)\n",
    "visualizeCells(sw_prf_num)\n",
    "plot(xt_prf*t_anal[end], sw_prf)\n",
    "axis([0, L_core, 0, 1.0])\n",
    "legend([\"Numerical\", \"Analytical\"])\n",
    "xlabel(\"Core length [m]\")\n",
    "ylabel(\"Water saturation [-]\")\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can see that the numerical solution is very close to the analytical solution. This must give a better match for the recovery curves as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fa4baf6bb50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# numerical solution (finite volume)\n",
    "(t_num, R_num, sw_prf)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj, Nx=500)\n",
    "\n",
    "# Analytical solution (BL)\n",
    "(xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "  muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "  k=perm_ave, swc=swc, sor=sor, kro0=kro0, no=no, \n",
    "  krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj)\n",
    "plot(t_anal, R_anal, \"o\", t_num, R_num)\n",
    "xlabel(\"time [s]\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "axis([25000, 50000, 0.40, 0.5])\n",
    "IJulia.clear_output()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.1",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
